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BASIC CIRCUIT ANALYSIS
UNIT-I
PART-A
1. What is a graph of network?
When all elements in a network are replaced by lines with circles of dos at both ends.
2. What is tree of a network?
It is an interconnected open set of branches which include all the nodes of the given
graph.
3. Give the properties of tree in a graph.
It consists of all the nodes of the graph
If the graph has N no of nodes the tree will have N-I branches
There will be no closed path in the tree
There can be many possible different trees for a given graph depending on the no
of nodes and branches.
4. Define Ohms Law.
The potential difference across any two ends of a conductor is directly proportional to the
current flowing between the two ends provided the temperature of the conductor remains
constant.
5. Define Quality factor.
The quality factor is defined as the ratio of maximum energy stored to the energy
dissipated in one period.
6. What are half power frequencies?
In RLC circuits the frequ ncies at which the power is half the max/min power are
called half power frequencies.
7. Define selectivity.
It is defined as the ratio of bandwidth and resonant frequency. 1
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8. Write the characteristics of series resonance.
At resonance impedance in min and equal to resistance therefore current is max. Before
resonant frequency the circuit behaves as capacitive circuit and above resonant frequency
the circuit will behave as inductive circuit. At resonance the magnitude of voltage across
the inductance and capacitance will be Q times the supply voltage but they are in phase
opposition.
9. What is anti resonance?
In RLC parallel circuit the current is min at resonance whereas in series resonance
the current is max. Therefore the parallel resonance is called anti resonance.
10. Write the characteristics of parallel resonance.
At resonance admittance in min and equal to conductance therefore the current is
min.
Below resonant frequency the circuits behave as inductive circuit and above resonant
frequency the circuit behaves as capacitive circuit.
At resonance the magnitude of current through inductance and capacitance will be
q times the current supplied by the source but they are in phase opposition.
11. Define KCL
KCL states that the algebraic sum of currents in node is zero.
12. Define KVL
KVL states that the algebraic sum of voltages in a closed path is zero.
13. What is meant by linear and nonlinear elements?
Linear element shows the linear characteristics of voltage Vs current.
Nonlinear element the current passing through it does not change linearity with the
linear change in applied voltage at a particular frequency.
14. What is meant by active and passive elements?
If a circuit element has the capability of enhancing the energy level of a signal
passing through it is called an active element.
Passive elements do not have any intrinsic means of signal boosting.
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15. What is meant by unilateral and bilateral elements?
If the magnitude of the current passing through an element is affected due to change
in the polarity of the applied voltage is called unilateral elements.
If the current magnitude remains the same even if the applied EMFs polarity is
changed is called bilateral elements.
16. What is a dual network?
In an electrical circuit itself there are pairs of terms, which can be interchanged to
get new circuits. Such pair of dual terms is given below
Current- Voltage
Open- Short
L-C
R-G
Series – Parallel
Voltage source- Current source
KCL-KVL
17. Give the steps to draw a Dual Network
In each loop of a network place a node
Draw the lines connecting adjacent nodes passing through each element and also to the
reference node.
18. Mention the disadvantages of Ohm’s Law.
It does not apply to all non metallic conductors
It also does not apply to non linear devices such as zener diode, vacuum tubes etc.
It is true for metal conductors at constant temperature. If the temperature changes
the law is not applicable.
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19. Compare series and parallel circuit.
S Series circuit Parallel circuit
No
1 The total effective resistance is the sum of the
individual resistance ie
Reff=R1+R2+……R n
The reciprocal of the total effective
resistance is the sum of the reciprocals of
individual resistance
1/Reff= 1/R1+1/R2+….1/R n
2 Only one path for the current flow
3 The current flowing through all the
resistances will be the same and equal to the
total current
4 The voltage is divided across each resistance
according to the value of resistance.
More than one path for the current to
flow
The current flowing through each
resistance is different
The voltage across each resistance is
same which will be equal to the input
voltage.
20. What is a node?
A node is a point in a network in which two or more elements have a
common connection.
21. What are the classificatio ns of Circuit elements?
Active element
Passive element
Lumped and distributed elements
Bilateral and unilateral elements
Linear and non linear elements.
22. What are dependent and independent sources?
The electrical energy supplied by dependent sources a source of electrical energy.
The electrical energy supplied by independent source does not depend on another
electrical source. They convert some energy in to electrical form.
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23. Define series and parallel connection.
If the resistances are connected end to end the combination is said to be series.
24. What is a super node?
The region surrounding a voltage source which connects the two nodes directly
called super node.
25. What is principle node?
The meeting point of three or more elements is called principle node.
26. What is a closed path?
A closed path which starts at a node and travels through some part of the circuit and
arrives at the same node without crossing the node or more than once.
27. State voltage division rule.
Voltage across a resistor in series circuit is equal to the total voltage across the series
elements multiplied by the value of that resistor divided by the total resistance of the series
elements.
28. State current division rule.
The current in any branch is equal to the ratio of the opposite parallel branch
resistances to the total resistance value, multiplied by the total current in the circuit.
29. Define mesh.
A mesh is defined as a lo op which does not contain any other loops within it.
30. What is a planar circuit?
A circuit is said to be non planar if it cannot be drawn on a plane surface without
crossovers.
31. Define super mesh.
The loop existing around a current source which is common to the two loops is called
super mesh.
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PART-B
1. Find the current through each branch by network reduction technique.
2. Calculate a) the equivalent resistances across the terminals of the supply, b) total
current supplied by the source and c) power delivered to 16 ohm resistor in the circuit
shown in figure.
3. In the circuit shown, determine the current through the 2 ohm resistor and the
total current delivered by the battery. Use Kirchhoff’s laws.
4. (i) Determine the current through 800 ohm resistor in the network shown in figure. (8)
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(ii) Find the power dissipated in 10 ohm resistor for the circuit shown in figure. (8)
5. (i) In the network shown below, find the current delivered by the battery. (10)
(ii) Discuss about voltage and current division principles.
(6) 6. (i) Explain :
Kirchoff laws. (4)
Dependent sources (2)
Source transformations
(2) with relevant
diagrams.
Voltage division and current division rule (4)
(ii) Calculate the resistance between the terminals A – B. (4)
7. i)Determine the value of V2 such that the current through the impedance
(3+j4) ohm is zero.
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ii) Find the current through branch a-b using mesh analysis shown in figure below.
8. Determine the mesh currents I1 and I2 for the given circuit shown below
9. Find the node voltages V1 and V2 and also the current supplied by the source for
the circuit shown below.
10. Find the nodal voltages in the circuit of figure.
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11. i) Using the node voltage analysis, find all the node voltages and currents in 1/3
ohm and 1/5 ohm resistances of figure.
ii) For the mesh-current analysis, explain the rules for constructing mesh
impedance matrix and solving the matrix equation [Z]I = V.
12. Solve for V1 and V2 using nodal method. Let V = 100V.
13. Using Mesh analysis, find current through 4 ohm resistor.
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14. Use nodal voltage method to find the voltages of nodes ‘m’ and ‘n’
and currents through j2 ohm and –j2 ohm reactance in the network
shown below.
15. For the circuit shown find the current I flowing through 2 ohm resistance using
loop analysis.
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UNIT II
1. Sate superposition theorem.
It states that the response of a linear circuit with multiple sources is given
by algebraic sum of response due to individual sources acting alone.
2. State Thevenins theorem
It states that any linear bilateral network can be replaced by a single current
source VTH, in series with single impedance Zth
3. State Norton’s theorem
It states that any linear bilateral network can be replaced by a single current
source, IN in parallel with single impedance Zth.
4. State maximum power transfer theorem.
Max power is transferred to load impedance if the load impedance is
the complex conjugate of the source impedance.
5. State reciprocity theorem.
It states that in a linear, bilateral single source circuit the ratio of excitation
to the response is constant w en the position of excitation and response are
interchanged.
6. State compensation theorem.
Let I be the current through an impedance Z in a brach of circuit.
It states that the change in current due to change in impedance in a branch
will be produced by a compensation voltage source in the same branch with
polarity opposing the original current.
7. State Millman’s theorem
It states that if a number of voltage sources with internal impedance are in
parallel then they can be combined to give a voltage source with an equivalent emf
and internal impedance.
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8. State Tellegen’s theorem.
It states that the summation of all the product of branch voltage and its current of
a circuit is zero.
9. State the steps to solve the super position theorem.
Take only one independent voltage or current source
Obtain the branch currents
Repeat the above for ther sources
To determine the net ranch current just adds the currents obtained above.
10. State the steps to solve the Thevenin’s theorem.
Remove the load resistance and find the open circuit voltage VOC
Deactivate the consta t sources (fro voltage source remove it by internal
resistance & for current source delete the source by OC) and find the internal
resistance (RTH) of the source side looking through the open circuited
load terminals
Obtain the Thevenin’s equivalent circuit by connecting VOC in series with RTH
Reconnect the load resistance across the load terminals.
11. State the steps to solve the Norton’s theorem.
Remove the load resistor and find the internal resistance of the source
N/W by deactivating the constant source.
Short the load terminals and find the short circuit current
Norton’s equivalent circuit is drawn by keeping R TH in parallel with ISC
12. What is the Load current in a Norton’s circuit?
IL= (ISC.RTH) / (RTH+RL)
13. What is the load current in Thevenin’s circuit? IL=
VOC / (RTH+RL)
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14. What is the maximum power in a circuit?
Max power:VO C
2
/4 RTH
15. Write some applications of maximum power transfer theorem.
Power amplifiers
Communication system
Microwave transmission
16. What is the limitation of superposition theorem?
This theorem is valid only for linear systems. This theorem can be applied for
calculating the current through or voltage across in particular element. But this
superposition theorem is not applicable for calculation of the power.
17. What are the limitations of maximum power transfer theorem?
The maximum efficiency can be obtained by using this theorem is only 50% .
It is because of 50% of the power is unnecessarily wasted in Rth.
Therefore this theorem only applicable for communication circuits and not for
power circuits where efficiency is greater importance rather than power delivered.
18. State voltgae division rule.
Voltage across a resistor in a series ciruict is equal to the total voltage across
elements mulitiplied by the value of that resistor divided by the total resistance of
the series elements.
V1=(R1)*V/ (R1+R2)
19. State current division rule.
Current in any branch is equal to the ratio of the opposite paralel branch resistance to
the total resistance value, multiplied by the total current in the circuit.
I1=(R2)*I/(R1+R2)
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20. Define source transformtion.
The current and voltage sources may be inter changed without affecting the remainder
of the circuit, this technique is the source transformation. It is the tool for simplifying the
circuit.
21. List the applications of Thevinins theorem.
It is applied to all linear circuits including electronic circuits represented by the
controlled source.
This theorem is useful when t is desired to know the effect of the response in network or
varying part of the network.
22. Explain the purpose of star delta transformation.
The transformation of a given set of resistances in star to delta or vice versa
proves extremely useful in circuit analysis and the apparent complexity of a
given circuit can sometime by very much reduced.
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PART – B
1. (i) Find the value of R and the current flowing through it in the circuit shown when
the current in the branch OA is zero. (8)
ii) Determine the Thevenin’s equivalent for the figure (8)
2. Derive expressions for star connected arms in terms of delta connected arms and delta
connected arms in terms of star connected arms. (16)
3. Determine Thevenin’s equivalent across the terminals AB for the circuit shown in figure
below. (16)
4. Find the Thevenins ’s equivalent circuit of the circuit shown below, to left of the terminals ab.
Then find the current through RL = 16 ohm and 36 ohm. (16)
5. i) Find the current through branch a-b network using Thevenin’s theorem. (8)
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ii) Find the current in each resistor using superposition principle of figure. (8)
6. i) Determine the Thevenin’s equivalent circuit. (8)
(ii) Determine the equivalent resistance across AB of the circuit shown in the figure below.
(8)
7. For the circuit shown, use sup rposition theorem to compute current I.
8. (i)Compute the current in 23 ohm resistor using super position theorem for the
circuit shown below. (8)
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(ii) Find the equivalent resistance between B and C in figure (8)
9. Using superposition theorem calculate current through (2+j3) ohm impedance branch of the
circuit shown.
10. i) For the circuit shown, determine the current in (2+j3) ohm by using
superposition theorem. (8)
ii) State and prove Norton’s theorem. (8)
11.i) Find the value of RL so that maximum power is delivered to
the load resistance shown in figure. (8)
ii) State and prove compensation theorem. (8)
12. Determine the maximum power delivered to the load in the circuit. (16)
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13. Find the value of impedance Z so that maximum power will be transferred from source to
load for the circuit shown. (16)
14. i) State and explain maximum power transfer theorem for variable Pure resistive load.
(8) ii) Using Norton’s theorem, find current through 6 ohm resistance shown in figure.
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UNIT III
RESONANCE AND COUPLED CIRCUITS
1. What is meant by Resonance?
An A.C circuit is said to be resonance if it behaves as a purely resistive circuit. The total
current drawn by the circuit is then in phase with the applied voltage, and the power factor will
then unity. Thus at resonance the equivalent complex impedance of the circuit has no j
component.
2. Write the expression for the resonant frequency of a RLC series
circuit. Resonant frequency fr=1/2π√LC
3. What is resonant frequency?
The frequency at which resonance occurs is called resonant frequency.
At resonant frequency XL=XC
4. Define series resonance.
A resonance occurs in RLC series circuit called series resonance. Under
resonance condition, the input current is in phase with applied voltage.
5. Define Quality factor.
The quality factor is defi ned as the ratio of maximum energy stored to the energy
dissipated in one period.
6. What are half power frequencies?
In RLC circuits the frequ ncies at which the power is half the max/min power are
called half power frequencies.
7. Write the characteristics of series resonance.
At resonance impedance in min and equal to resistance therefore current is max.
Before resonant frequency the circuit behaves as capacitive circuit and above
resonant frequency the circuit will behave as inductive circuit.
At resonance the magnitude of voltage across the inductance and capacitance will be Q
times the supply voltage but they are in phase opposition.
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8. Define selectivity.
It is defined as the ratio of bandwidth and resonant frequency.
9. What is anti resonance?
In RLC parallel circuit the current is min at resonance whereas in series resonance
the current is max. Therefore the parallel resonance is called anti resonance.
10. Write the characteristics of parallel resonance.
At resonance admittance in min and equal to conductance therefore the current is
min.
Below resonant frequency the circuits behave as inductive circuit and above resonant
frequency the circuit behaves as capacitive circuit.
At resonance the magnitude of current through inductance and capacitance will be
q times the current supplied by the source but they are in phase opposition.
11. What is Bandwidth and sel ctivity?
The frequency band within the limits of lower and upper half frequency is called
bandwidth.
BW=f2-f1
Selectivity is the ratio of fr to the bandwidth
Selectivity= fr / (f2-f1)
12. What are coupled circuits?
It refers to circuit involving elements with magnetic coupling. If the flux produced by an
element of a circuit links other elements of the same circuit then the elements are said to be
magnetic coupling.
13. What are coupled circuits?
When two or more coils are linked by magnetic flux, then the coils are
called coupled circuits.
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14. State the properties of a series RLC circuit.
The applied voltage and the resulting current are in phase, when also means than
the p.f of RLC circuit is unity.
The net reactance is zero at resonance and the impedance does not have the resistive
part only.
The current in the circuit is max: and is V/R amperes
At resonance the circuit has got minimum impedance and max: curre nt
Frequency of resonance is given by fr=1/(2π√LC)
15. State the properties of a parallel RLC circuit.
PF is unity
Current at resonance is (V/(L/RC)) and is in phase with the applied
voltage. The value of current at resonance is minimum.
Net impedance at resonance is max: & is equal to L/RC
The admittance is min: and the net susceptance is zero at resonance.
16. Define self inductance.
When permeability is constant the self inductance of a coil is defined as the ratio of
flux linkage and current.
17. Define mutual inductance.
When permeability is constant the mutual inductance between two coupled coils is
defined as the ratio of flux linkage in one coil due to common flux and current through another
coil.
18. Define coefficient of coupling.
In coupled coils the coefficient of coupling is defined as the raction of the total
flux produced by one coil linking another coil.
19. What is DOT convention?
The sign of mutual induced emf depends on the winding sense and the current through the
coil. The winding sense is decided by the manufacturer and to inform the user about the winding
sense a dot is placed at one end of each coil. When current enter at dotted end in one coil then the
mutual induced emf in the other coil is positive at dot end.
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21. State dot rule for coupled c rcuit.
It states that in coupled coils current entering at the dotted terminal of one coil induce
an emf in second coil which is +ve at dotted terminal of second coil.
Current entering at the un dotted terminal of one coil induce an emf in second
coil which is +ve at un dotted terminal of second coil.
22. Define coefficient of coupling.
The amount of coupling between to inductively coupled coils is expressed in terms of
the coefficient of coupling.
K=M/√L1L2
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PART – B
1. (i) Derive bandwidth for a series RLC circuit as a function of resonant frequency.(16)
2. (i) For the circuit below, find the value of ω so that current and source emf are
in phase. Also find the current at this frequency. (8)
(ii) Discuss the characteristics of parallel resonance of a circuit having G,L and C. 8)
3. (i) A Pure resistor, a pure capacitor and a pure inductor are connected in parallel across a 50Hz
supply, find the impedance of the circuit as seen by the supply. Also find the resonant frequency.
(8)
(ii) When connected to a 230V, 50Hz single phase supply, a coil takes 10kVA and 8kVAR.
For this coil calculate resistance, inductance of coil and power consumed.(8)
4. (i) In an RLC series circuit if ω1 and ω2 are two frequencies at which the magnitude of
the current is the same and if ωr is the resonant frequency, prove that ω2 r = ω1ω2.
(ii) A series RLC circuit has Q = 75 and a pass band (between half power frequencies) of 160
Hz. Calculate the resonant frequency and the upper and lower frequencies of the pass band. (8)
5. (i) Explain and derive the relationships for bandwidth and half power frequencies of RLC
series circuit. (8)
(ii) Determine the quality facto of a coil R = 10 ohm, L = 0.1H and C = 10Μf (8)
6. A series RLC circuit has R=20 ohm, L=0.005H and C = 0.2 x 10-6 F. It is fed from a 100V
variable frequency source. Find i) frequency at which current is maximum ii) impedance at this
frequency and iii) voltage across inductance at this frequency.
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7. A series RLC circuit consists of R=100 ohm, L = 0.02 H and C = 0.02 microfarad. Calculate
frequency of resonance. A variable frequency sinusoidal voltage of constant RMS value of 50V
is applied to the circuit. Find the frequency at which voltage across L and C is maximum. Also
calculate voltage across L and C is maximum. Also calculate voltages across L and C at
frequency of resonance. Find maximum current in the circuit. (16)
8. In the parallel RLC circuit, calculate resonant frequency, bandwidth, Q-factor and power
dissipated at half power frequencies. (16)
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UNIT IV
TRANSIENT RESPONSE FOR DC CIRCUITS
1. What is transient state?
If a network contains energy storage elements, with change in excitation, the current
and voltage change from one state to other state the behavior of the voltage or current when it
is changed from one state to another state is called transient state.
2. What is transient time?
The time taken for the circuit to change from one steady state to another steady
state is called transient time.
3. What is transient response?
The storage elements deliver their energy to the resistances, hence the response
changes with time, get sturated after sometime, and are referred to the transient response.
4. Define time constant of RLC circuit.
The time taken to reach 63.2% of final value in a RL circuit is called the time constant
of RL circuit.
Time constant=L/R
5. Define time constant of RC circuit.
The time to taken to reach 36.8% of initial current in an RC circuit is called the
time constant of RC circuit.
Time constant=
RC
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6. What is meant by natural frequency?
If the damping is made zero then the response oscillates with natural frequency
without any opposition, such a frequency is called natural frequency of oscillations.
7. Define damping ratio.
It is the ratio orf actual resistance in the circuit to the critical resistance.
8. Write down the condition, for the response of RLC series circuit to be under
damped for step input.
The condition for the reponse of RLC series circuit to be under damped step input is
(R/2L)
2
>(1/LC)
9. Write down the condition fo the response of RLC sereis circuit to be over
damped for step input.
The condition for the response of RLC series circuit to be over damped for step input
is,
(R/2L)
2
>(1/LC)
10. Write down the few applications of RL, RC, RLC circuits.
Coupling circuits
Phase shift circuits
Filters
Resonant circuits
AC bridge circuits
Transformers
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11. Define transient response.
The transient response is defined as the response or output of a circuit from the instant
of switching to attainment of steady state.
12. What is natural response?
The response of a circuit due to stored energy alone without external source is
called natural response or source free response.
13. What is forced response?
The response of the circuit due to the external source is called forced response.
14. Define apparent power.
The apparent power is defined as the product of magnitude of voltage and
magnitude of current.
15. What is power factor and reactive power?
The power factor is defined as the cosine of the phase difference between voltage and
current.
Power factor= cos
The reactive power of the circuit is defined as the sine of the phase angle.
Reactive power= sin
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PART – B
1. In the circuit of the figure shown below, find the expression for the transient current and the
initial rate of growth of the transient current (16)
2. In the circuit shown in figure, switch S is in position 1 for a long time and brought to
position 2 at time t=0. Determine the circuit current. (16)
3. A resistance R and 2 microfarad capacitor are connected in series across a 200V direct supply.
Across the capacitor is a neon lamp that strikes at 120V. Calculate R to make the lamp strike 5
sec after the switch has been closed. If R = 5Megohm, how long will it take the lamp to strike?
4. A Series RLC circuits has R=50 ohm, L= 0.2H, and C = 50 microfarad. Constant voltage of
100V is impressed upon the circuit at t=0. Find the expression for the transient current assuming
initially relaxed condit ons.
5. A Series RLC circuits with R=300 ohm, L=1H and C=100x10-6 F has a constant voltage of
50V applied to it at t= 0. Find the maximum value of current ( Assume zero initial conditions)
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6. A step voltage V(t) = 100 u(t) is applied to a series RLC circuit with L=10H, R=2ohm and C=
5F. The initial current in the circuit is zero but there is an initial voltage of 50V on the capacitor
in a direction which opposes the applied source. Find the expression for the current in the circuit.
7. For a source free RLC series circuit, the initial voltage across C is 10V and the initial current
through L is zero. If L = 20mH, C=0.5 microfarad and R=100 ohm. Evaluate i(t).
8. For the circuit shown in figure, find the voltage across the resistor 0.5 ohm when the switch, S
is opened at t=0. Assume that there is no charge on the capacitor and no current in the inductor
before switching
9. In the circuit shown in figure, find the current i. Assume that initial charge across the
capacitor is zero.
10. In the circuit shown in figure, the switch is closed at time t=0. Obtain i(t). Assume
zero current through inductor L and zero charge across C before closing the switch.
11. Derive an expression for current response of RLC series circuit transient. (16)
29
V.MOHAMED IBRAHIM AP/EEE
www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
UNIT V
THREE PHASE CIRCUITS
PART-A
1. Define line current and phase current.
The current flowing through the line is called line current
The current flowing through the phase is called phase current
2. Define line and phase voltag
The voltage between two lines is called the line voltage
The voltage between any line and the neutral point is called phase voltage.
3. Give the line and phase values in star connection
The relation between line and phase voltage in star connection is
EL=√3Eph
The relation between line current and phase current in a star connection is
IL=Iph
4. Give the line and phase values in delta connection
The relation between line voltage and phase voltage in a delta connection is
EL=Eph
The relation between line current and phase current in delta connection is
IL=√3Iph
30
V.MOHAMED IBRAHIM AP/EEE
www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
5. Write few methods available for measuring in 3-phase load.
One wattmeter method
Two wattmeter method
Three wattmeter method
6. List the methods used for power measurement with single wattmeter
Potential lead shift method
T- method
Artificial neutral method
Current transformer method
7. List the methods for unbalanced star connected load
Equivalents delta method
Mesh method
Neutral voltage displacement method
8. Write the methods of conne ctions of 3 phase windings?
Independent connection
Star connection and
Delta connection
31
V.MOHAMED IBRAHIM AP/EEE
www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
PART – B
1. With a neat circuit and phasor diagram explain the three phase power measurement by two
wattmeter methods.
2. (i) A symmetrical three phase 400V system supplies a balanced delta connected load. The
current in each branch circuit is 20A and phase angle 40° (lag) calculate the line current and total
power. (8)
(ii) A three phase delta connected load has Zab = (100+j0) ohms, Zbc = (-j100) ohms and Zca =
(70.7 =j70.7) ohms is connected to a balanced 3 phase 400V supply. Determine the line currents
Ia,Ib and Ic. Assume the phase sequence abc. (8)
3. (i) A balanced three phase star connected load with impedance 8+j6 ohm per phase is
connected across a symmetrical 400V three phase 50Hz supply. Determine the line current,
power factor of the load and total power. (8)
(ii) An alternating current is expressed as i=14.14 sin 314t. Determine rms current, frequency
and instantaneous current hen t =0.02ms. (8)
4. (i) A balanced star connected load of 4+j3 ohm per phase is connected to a 400V, 3 phase,
50Hz supply. Find the line current, power factor, power, reactive volt ampere and total volt
ampere. (8)
(ii) A Voltage source 100V with resistance of 10 ohms and inductance 50 mH, a capacitor 50
microfarad are connected in series. Calculate the impedance when the frequency is (i) 50HZ (ii)
500Hz (iii) the power factor at 100Hz. (8)
5. (i) Three impedances Z1 = 3∟45° ohm, Z2 = 10 √2∟45° ohm, Z3 = 5 ∟-90° ohm are
connected in series. Calculate applied voltage if voltage across Z1 = 27∟-10° V. (8)
(ii) A delta connected load as shown in figure is connected across 3 phase 100 volt supply.
Determine all line currents. (8)
32
V.MOHAMED IBRAHIM AP/EEE
www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com

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Circuit Theory Question Bank

  • 1. BASIC CIRCUIT ANALYSIS UNIT-I PART-A 1. What is a graph of network? When all elements in a network are replaced by lines with circles of dos at both ends. 2. What is tree of a network? It is an interconnected open set of branches which include all the nodes of the given graph. 3. Give the properties of tree in a graph. It consists of all the nodes of the graph If the graph has N no of nodes the tree will have N-I branches There will be no closed path in the tree There can be many possible different trees for a given graph depending on the no of nodes and branches. 4. Define Ohms Law. The potential difference across any two ends of a conductor is directly proportional to the current flowing between the two ends provided the temperature of the conductor remains constant. 5. Define Quality factor. The quality factor is defined as the ratio of maximum energy stored to the energy dissipated in one period. 6. What are half power frequencies? In RLC circuits the frequ ncies at which the power is half the max/min power are called half power frequencies. 7. Define selectivity. It is defined as the ratio of bandwidth and resonant frequency. 1 V.MOHAMED IBRAHIM AP/EEE Vidyarthiplus - Anna University Students Online Community - Question Bank www.Vidyarthiplus.com Vidyarthiplus - Anna University Students Online Community - Question Bank www.Vidyarthiplus.com www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
  • 2. 8. Write the characteristics of series resonance. At resonance impedance in min and equal to resistance therefore current is max. Before resonant frequency the circuit behaves as capacitive circuit and above resonant frequency the circuit will behave as inductive circuit. At resonance the magnitude of voltage across the inductance and capacitance will be Q times the supply voltage but they are in phase opposition. 9. What is anti resonance? In RLC parallel circuit the current is min at resonance whereas in series resonance the current is max. Therefore the parallel resonance is called anti resonance. 10. Write the characteristics of parallel resonance. At resonance admittance in min and equal to conductance therefore the current is min. Below resonant frequency the circuits behave as inductive circuit and above resonant frequency the circuit behaves as capacitive circuit. At resonance the magnitude of current through inductance and capacitance will be q times the current supplied by the source but they are in phase opposition. 11. Define KCL KCL states that the algebraic sum of currents in node is zero. 12. Define KVL KVL states that the algebraic sum of voltages in a closed path is zero. 13. What is meant by linear and nonlinear elements? Linear element shows the linear characteristics of voltage Vs current. Nonlinear element the current passing through it does not change linearity with the linear change in applied voltage at a particular frequency. 14. What is meant by active and passive elements? If a circuit element has the capability of enhancing the energy level of a signal passing through it is called an active element. Passive elements do not have any intrinsic means of signal boosting. V.MOHAMED IBRAHIM AP/EEE www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
  • 3. 15. What is meant by unilateral and bilateral elements? If the magnitude of the current passing through an element is affected due to change in the polarity of the applied voltage is called unilateral elements. If the current magnitude remains the same even if the applied EMFs polarity is changed is called bilateral elements. 16. What is a dual network? In an electrical circuit itself there are pairs of terms, which can be interchanged to get new circuits. Such pair of dual terms is given below Current- Voltage Open- Short L-C R-G Series – Parallel Voltage source- Current source KCL-KVL 17. Give the steps to draw a Dual Network In each loop of a network place a node Draw the lines connecting adjacent nodes passing through each element and also to the reference node. 18. Mention the disadvantages of Ohm’s Law. It does not apply to all non metallic conductors It also does not apply to non linear devices such as zener diode, vacuum tubes etc. It is true for metal conductors at constant temperature. If the temperature changes the law is not applicable. 3 V.MOHAMED IBRAHIM AP/EEE www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
  • 4. 19. Compare series and parallel circuit. S Series circuit Parallel circuit No 1 The total effective resistance is the sum of the individual resistance ie Reff=R1+R2+……R n The reciprocal of the total effective resistance is the sum of the reciprocals of individual resistance 1/Reff= 1/R1+1/R2+….1/R n 2 Only one path for the current flow 3 The current flowing through all the resistances will be the same and equal to the total current 4 The voltage is divided across each resistance according to the value of resistance. More than one path for the current to flow The current flowing through each resistance is different The voltage across each resistance is same which will be equal to the input voltage. 20. What is a node? A node is a point in a network in which two or more elements have a common connection. 21. What are the classificatio ns of Circuit elements? Active element Passive element Lumped and distributed elements Bilateral and unilateral elements Linear and non linear elements. 22. What are dependent and independent sources? The electrical energy supplied by dependent sources a source of electrical energy. The electrical energy supplied by independent source does not depend on another electrical source. They convert some energy in to electrical form. 4 V.MOHAMED IBRAHIM AP/EEE www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
  • 5. 23. Define series and parallel connection. If the resistances are connected end to end the combination is said to be series. 24. What is a super node? The region surrounding a voltage source which connects the two nodes directly called super node. 25. What is principle node? The meeting point of three or more elements is called principle node. 26. What is a closed path? A closed path which starts at a node and travels through some part of the circuit and arrives at the same node without crossing the node or more than once. 27. State voltage division rule. Voltage across a resistor in series circuit is equal to the total voltage across the series elements multiplied by the value of that resistor divided by the total resistance of the series elements. 28. State current division rule. The current in any branch is equal to the ratio of the opposite parallel branch resistances to the total resistance value, multiplied by the total current in the circuit. 29. Define mesh. A mesh is defined as a lo op which does not contain any other loops within it. 30. What is a planar circuit? A circuit is said to be non planar if it cannot be drawn on a plane surface without crossovers. 31. Define super mesh. The loop existing around a current source which is common to the two loops is called super mesh. 5 V.MOHAMED IBRAHIM AP/EEE www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
  • 6. PART-B 1. Find the current through each branch by network reduction technique. 2. Calculate a) the equivalent resistances across the terminals of the supply, b) total current supplied by the source and c) power delivered to 16 ohm resistor in the circuit shown in figure. 3. In the circuit shown, determine the current through the 2 ohm resistor and the total current delivered by the battery. Use Kirchhoff’s laws. 4. (i) Determine the current through 800 ohm resistor in the network shown in figure. (8) 6 V.MOHAMED IBRAHIM AP/EEE www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
  • 7. (ii) Find the power dissipated in 10 ohm resistor for the circuit shown in figure. (8) 5. (i) In the network shown below, find the current delivered by the battery. (10) (ii) Discuss about voltage and current division principles. (6) 6. (i) Explain : Kirchoff laws. (4) Dependent sources (2) Source transformations (2) with relevant diagrams. Voltage division and current division rule (4) (ii) Calculate the resistance between the terminals A – B. (4) 7. i)Determine the value of V2 such that the current through the impedance (3+j4) ohm is zero. 7 V.MOHAMED IBRAHIM AP/EEE www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
  • 8. ii) Find the current through branch a-b using mesh analysis shown in figure below. 8. Determine the mesh currents I1 and I2 for the given circuit shown below 9. Find the node voltages V1 and V2 and also the current supplied by the source for the circuit shown below. 10. Find the nodal voltages in the circuit of figure. 8 V.MOHAMED IBRAHIM AP/EEE www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
  • 9. 11. i) Using the node voltage analysis, find all the node voltages and currents in 1/3 ohm and 1/5 ohm resistances of figure. ii) For the mesh-current analysis, explain the rules for constructing mesh impedance matrix and solving the matrix equation [Z]I = V. 12. Solve for V1 and V2 using nodal method. Let V = 100V. 13. Using Mesh analysis, find current through 4 ohm resistor. 9 V.MOHAMED IBRAHIM AP/EEE www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
  • 10. 14. Use nodal voltage method to find the voltages of nodes ‘m’ and ‘n’ and currents through j2 ohm and –j2 ohm reactance in the network shown below. 15. For the circuit shown find the current I flowing through 2 ohm resistance using loop analysis. 10 V.MOHAMED IBRAHIM AP/EEE www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
  • 11. UNIT II 1. Sate superposition theorem. It states that the response of a linear circuit with multiple sources is given by algebraic sum of response due to individual sources acting alone. 2. State Thevenins theorem It states that any linear bilateral network can be replaced by a single current source VTH, in series with single impedance Zth 3. State Norton’s theorem It states that any linear bilateral network can be replaced by a single current source, IN in parallel with single impedance Zth. 4. State maximum power transfer theorem. Max power is transferred to load impedance if the load impedance is the complex conjugate of the source impedance. 5. State reciprocity theorem. It states that in a linear, bilateral single source circuit the ratio of excitation to the response is constant w en the position of excitation and response are interchanged. 6. State compensation theorem. Let I be the current through an impedance Z in a brach of circuit. It states that the change in current due to change in impedance in a branch will be produced by a compensation voltage source in the same branch with polarity opposing the original current. 7. State Millman’s theorem It states that if a number of voltage sources with internal impedance are in parallel then they can be combined to give a voltage source with an equivalent emf and internal impedance. 11 V.MOHAMED IBRAHIM AP/EEE www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
  • 12. 8. State Tellegen’s theorem. It states that the summation of all the product of branch voltage and its current of a circuit is zero. 9. State the steps to solve the super position theorem. Take only one independent voltage or current source Obtain the branch currents Repeat the above for ther sources To determine the net ranch current just adds the currents obtained above. 10. State the steps to solve the Thevenin’s theorem. Remove the load resistance and find the open circuit voltage VOC Deactivate the consta t sources (fro voltage source remove it by internal resistance & for current source delete the source by OC) and find the internal resistance (RTH) of the source side looking through the open circuited load terminals Obtain the Thevenin’s equivalent circuit by connecting VOC in series with RTH Reconnect the load resistance across the load terminals. 11. State the steps to solve the Norton’s theorem. Remove the load resistor and find the internal resistance of the source N/W by deactivating the constant source. Short the load terminals and find the short circuit current Norton’s equivalent circuit is drawn by keeping R TH in parallel with ISC 12. What is the Load current in a Norton’s circuit? IL= (ISC.RTH) / (RTH+RL) 13. What is the load current in Thevenin’s circuit? IL= VOC / (RTH+RL) 12 V.MOHAMED IBRAHIM AP/EEE www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
  • 13. 14. What is the maximum power in a circuit? Max power:VO C 2 /4 RTH 15. Write some applications of maximum power transfer theorem. Power amplifiers Communication system Microwave transmission 16. What is the limitation of superposition theorem? This theorem is valid only for linear systems. This theorem can be applied for calculating the current through or voltage across in particular element. But this superposition theorem is not applicable for calculation of the power. 17. What are the limitations of maximum power transfer theorem? The maximum efficiency can be obtained by using this theorem is only 50% . It is because of 50% of the power is unnecessarily wasted in Rth. Therefore this theorem only applicable for communication circuits and not for power circuits where efficiency is greater importance rather than power delivered. 18. State voltgae division rule. Voltage across a resistor in a series ciruict is equal to the total voltage across elements mulitiplied by the value of that resistor divided by the total resistance of the series elements. V1=(R1)*V/ (R1+R2) 19. State current division rule. Current in any branch is equal to the ratio of the opposite paralel branch resistance to the total resistance value, multiplied by the total current in the circuit. I1=(R2)*I/(R1+R2) V.MOHAMED IBRAHIM AP/EEE www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
  • 14. 20. Define source transformtion. The current and voltage sources may be inter changed without affecting the remainder of the circuit, this technique is the source transformation. It is the tool for simplifying the circuit. 21. List the applications of Thevinins theorem. It is applied to all linear circuits including electronic circuits represented by the controlled source. This theorem is useful when t is desired to know the effect of the response in network or varying part of the network. 22. Explain the purpose of star delta transformation. The transformation of a given set of resistances in star to delta or vice versa proves extremely useful in circuit analysis and the apparent complexity of a given circuit can sometime by very much reduced. 14 V.MOHAMED IBRAHIM AP/EEE www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
  • 15. PART – B 1. (i) Find the value of R and the current flowing through it in the circuit shown when the current in the branch OA is zero. (8) ii) Determine the Thevenin’s equivalent for the figure (8) 2. Derive expressions for star connected arms in terms of delta connected arms and delta connected arms in terms of star connected arms. (16) 3. Determine Thevenin’s equivalent across the terminals AB for the circuit shown in figure below. (16) 4. Find the Thevenins ’s equivalent circuit of the circuit shown below, to left of the terminals ab. Then find the current through RL = 16 ohm and 36 ohm. (16) 5. i) Find the current through branch a-b network using Thevenin’s theorem. (8) 15 V.MOHAMED IBRAHIM AP/EEE www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
  • 16. ii) Find the current in each resistor using superposition principle of figure. (8) 6. i) Determine the Thevenin’s equivalent circuit. (8) (ii) Determine the equivalent resistance across AB of the circuit shown in the figure below. (8) 7. For the circuit shown, use sup rposition theorem to compute current I. 8. (i)Compute the current in 23 ohm resistor using super position theorem for the circuit shown below. (8) 16 V.MOHAMED IBRAHIM AP/EEE www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
  • 17. (ii) Find the equivalent resistance between B and C in figure (8) 9. Using superposition theorem calculate current through (2+j3) ohm impedance branch of the circuit shown. 10. i) For the circuit shown, determine the current in (2+j3) ohm by using superposition theorem. (8) ii) State and prove Norton’s theorem. (8) 11.i) Find the value of RL so that maximum power is delivered to the load resistance shown in figure. (8) ii) State and prove compensation theorem. (8) 12. Determine the maximum power delivered to the load in the circuit. (16) 17 V.MOHAMED IBRAHIM AP/EEE www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
  • 18. 13. Find the value of impedance Z so that maximum power will be transferred from source to load for the circuit shown. (16) 14. i) State and explain maximum power transfer theorem for variable Pure resistive load. (8) ii) Using Norton’s theorem, find current through 6 ohm resistance shown in figure. 18 V.MOHAMED IBRAHIM AP/EEE www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
  • 19. UNIT III RESONANCE AND COUPLED CIRCUITS 1. What is meant by Resonance? An A.C circuit is said to be resonance if it behaves as a purely resistive circuit. The total current drawn by the circuit is then in phase with the applied voltage, and the power factor will then unity. Thus at resonance the equivalent complex impedance of the circuit has no j component. 2. Write the expression for the resonant frequency of a RLC series circuit. Resonant frequency fr=1/2π√LC 3. What is resonant frequency? The frequency at which resonance occurs is called resonant frequency. At resonant frequency XL=XC 4. Define series resonance. A resonance occurs in RLC series circuit called series resonance. Under resonance condition, the input current is in phase with applied voltage. 5. Define Quality factor. The quality factor is defi ned as the ratio of maximum energy stored to the energy dissipated in one period. 6. What are half power frequencies? In RLC circuits the frequ ncies at which the power is half the max/min power are called half power frequencies. 7. Write the characteristics of series resonance. At resonance impedance in min and equal to resistance therefore current is max. Before resonant frequency the circuit behaves as capacitive circuit and above resonant frequency the circuit will behave as inductive circuit. At resonance the magnitude of voltage across the inductance and capacitance will be Q times the supply voltage but they are in phase opposition. 19 V.MOHAMED IBRAHIM AP/EEE www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
  • 20. 8. Define selectivity. It is defined as the ratio of bandwidth and resonant frequency. 9. What is anti resonance? In RLC parallel circuit the current is min at resonance whereas in series resonance the current is max. Therefore the parallel resonance is called anti resonance. 10. Write the characteristics of parallel resonance. At resonance admittance in min and equal to conductance therefore the current is min. Below resonant frequency the circuits behave as inductive circuit and above resonant frequency the circuit behaves as capacitive circuit. At resonance the magnitude of current through inductance and capacitance will be q times the current supplied by the source but they are in phase opposition. 11. What is Bandwidth and sel ctivity? The frequency band within the limits of lower and upper half frequency is called bandwidth. BW=f2-f1 Selectivity is the ratio of fr to the bandwidth Selectivity= fr / (f2-f1) 12. What are coupled circuits? It refers to circuit involving elements with magnetic coupling. If the flux produced by an element of a circuit links other elements of the same circuit then the elements are said to be magnetic coupling. 13. What are coupled circuits? When two or more coils are linked by magnetic flux, then the coils are called coupled circuits. 20 V.MOHAMED IBRAHIM AP/EEE www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
  • 21. 14. State the properties of a series RLC circuit. The applied voltage and the resulting current are in phase, when also means than the p.f of RLC circuit is unity. The net reactance is zero at resonance and the impedance does not have the resistive part only. The current in the circuit is max: and is V/R amperes At resonance the circuit has got minimum impedance and max: curre nt Frequency of resonance is given by fr=1/(2π√LC) 15. State the properties of a parallel RLC circuit. PF is unity Current at resonance is (V/(L/RC)) and is in phase with the applied voltage. The value of current at resonance is minimum. Net impedance at resonance is max: & is equal to L/RC The admittance is min: and the net susceptance is zero at resonance. 16. Define self inductance. When permeability is constant the self inductance of a coil is defined as the ratio of flux linkage and current. 17. Define mutual inductance. When permeability is constant the mutual inductance between two coupled coils is defined as the ratio of flux linkage in one coil due to common flux and current through another coil. 18. Define coefficient of coupling. In coupled coils the coefficient of coupling is defined as the raction of the total flux produced by one coil linking another coil. 19. What is DOT convention? The sign of mutual induced emf depends on the winding sense and the current through the coil. The winding sense is decided by the manufacturer and to inform the user about the winding sense a dot is placed at one end of each coil. When current enter at dotted end in one coil then the mutual induced emf in the other coil is positive at dot end. 21 V.MOHAMED IBRAHIM AP/EEE www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
  • 22. 21. State dot rule for coupled c rcuit. It states that in coupled coils current entering at the dotted terminal of one coil induce an emf in second coil which is +ve at dotted terminal of second coil. Current entering at the un dotted terminal of one coil induce an emf in second coil which is +ve at un dotted terminal of second coil. 22. Define coefficient of coupling. The amount of coupling between to inductively coupled coils is expressed in terms of the coefficient of coupling. K=M/√L1L2 22 V.MOHAMED IBRAHIM AP/EEE www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
  • 23. PART – B 1. (i) Derive bandwidth for a series RLC circuit as a function of resonant frequency.(16) 2. (i) For the circuit below, find the value of ω so that current and source emf are in phase. Also find the current at this frequency. (8) (ii) Discuss the characteristics of parallel resonance of a circuit having G,L and C. 8) 3. (i) A Pure resistor, a pure capacitor and a pure inductor are connected in parallel across a 50Hz supply, find the impedance of the circuit as seen by the supply. Also find the resonant frequency. (8) (ii) When connected to a 230V, 50Hz single phase supply, a coil takes 10kVA and 8kVAR. For this coil calculate resistance, inductance of coil and power consumed.(8) 4. (i) In an RLC series circuit if ω1 and ω2 are two frequencies at which the magnitude of the current is the same and if ωr is the resonant frequency, prove that ω2 r = ω1ω2. (ii) A series RLC circuit has Q = 75 and a pass band (between half power frequencies) of 160 Hz. Calculate the resonant frequency and the upper and lower frequencies of the pass band. (8) 5. (i) Explain and derive the relationships for bandwidth and half power frequencies of RLC series circuit. (8) (ii) Determine the quality facto of a coil R = 10 ohm, L = 0.1H and C = 10Μf (8) 6. A series RLC circuit has R=20 ohm, L=0.005H and C = 0.2 x 10-6 F. It is fed from a 100V variable frequency source. Find i) frequency at which current is maximum ii) impedance at this frequency and iii) voltage across inductance at this frequency. 23 V.MOHAMED IBRAHIM AP/EEE www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
  • 24. 7. A series RLC circuit consists of R=100 ohm, L = 0.02 H and C = 0.02 microfarad. Calculate frequency of resonance. A variable frequency sinusoidal voltage of constant RMS value of 50V is applied to the circuit. Find the frequency at which voltage across L and C is maximum. Also calculate voltage across L and C is maximum. Also calculate voltages across L and C at frequency of resonance. Find maximum current in the circuit. (16) 8. In the parallel RLC circuit, calculate resonant frequency, bandwidth, Q-factor and power dissipated at half power frequencies. (16) 24 V.MOHAMED IBRAHIM AP/EEE www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
  • 25. UNIT IV TRANSIENT RESPONSE FOR DC CIRCUITS 1. What is transient state? If a network contains energy storage elements, with change in excitation, the current and voltage change from one state to other state the behavior of the voltage or current when it is changed from one state to another state is called transient state. 2. What is transient time? The time taken for the circuit to change from one steady state to another steady state is called transient time. 3. What is transient response? The storage elements deliver their energy to the resistances, hence the response changes with time, get sturated after sometime, and are referred to the transient response. 4. Define time constant of RLC circuit. The time taken to reach 63.2% of final value in a RL circuit is called the time constant of RL circuit. Time constant=L/R 5. Define time constant of RC circuit. The time to taken to reach 36.8% of initial current in an RC circuit is called the time constant of RC circuit. Time constant= RC 25 V.MOHAMED IBRAHIM AP/EEE www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
  • 26. 6. What is meant by natural frequency? If the damping is made zero then the response oscillates with natural frequency without any opposition, such a frequency is called natural frequency of oscillations. 7. Define damping ratio. It is the ratio orf actual resistance in the circuit to the critical resistance. 8. Write down the condition, for the response of RLC series circuit to be under damped for step input. The condition for the reponse of RLC series circuit to be under damped step input is (R/2L) 2 >(1/LC) 9. Write down the condition fo the response of RLC sereis circuit to be over damped for step input. The condition for the response of RLC series circuit to be over damped for step input is, (R/2L) 2 >(1/LC) 10. Write down the few applications of RL, RC, RLC circuits. Coupling circuits Phase shift circuits Filters Resonant circuits AC bridge circuits Transformers 26 V.MOHAMED IBRAHIM AP/EEE www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
  • 27. 11. Define transient response. The transient response is defined as the response or output of a circuit from the instant of switching to attainment of steady state. 12. What is natural response? The response of a circuit due to stored energy alone without external source is called natural response or source free response. 13. What is forced response? The response of the circuit due to the external source is called forced response. 14. Define apparent power. The apparent power is defined as the product of magnitude of voltage and magnitude of current. 15. What is power factor and reactive power? The power factor is defined as the cosine of the phase difference between voltage and current. Power factor= cos The reactive power of the circuit is defined as the sine of the phase angle. Reactive power= sin 27 V.MOHAMED IBRAHIM AP/EEE www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
  • 28. PART – B 1. In the circuit of the figure shown below, find the expression for the transient current and the initial rate of growth of the transient current (16) 2. In the circuit shown in figure, switch S is in position 1 for a long time and brought to position 2 at time t=0. Determine the circuit current. (16) 3. A resistance R and 2 microfarad capacitor are connected in series across a 200V direct supply. Across the capacitor is a neon lamp that strikes at 120V. Calculate R to make the lamp strike 5 sec after the switch has been closed. If R = 5Megohm, how long will it take the lamp to strike? 4. A Series RLC circuits has R=50 ohm, L= 0.2H, and C = 50 microfarad. Constant voltage of 100V is impressed upon the circuit at t=0. Find the expression for the transient current assuming initially relaxed condit ons. 5. A Series RLC circuits with R=300 ohm, L=1H and C=100x10-6 F has a constant voltage of 50V applied to it at t= 0. Find the maximum value of current ( Assume zero initial conditions) 28 V.MOHAMED IBRAHIM AP/EEE www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
  • 29. 6. A step voltage V(t) = 100 u(t) is applied to a series RLC circuit with L=10H, R=2ohm and C= 5F. The initial current in the circuit is zero but there is an initial voltage of 50V on the capacitor in a direction which opposes the applied source. Find the expression for the current in the circuit. 7. For a source free RLC series circuit, the initial voltage across C is 10V and the initial current through L is zero. If L = 20mH, C=0.5 microfarad and R=100 ohm. Evaluate i(t). 8. For the circuit shown in figure, find the voltage across the resistor 0.5 ohm when the switch, S is opened at t=0. Assume that there is no charge on the capacitor and no current in the inductor before switching 9. In the circuit shown in figure, find the current i. Assume that initial charge across the capacitor is zero. 10. In the circuit shown in figure, the switch is closed at time t=0. Obtain i(t). Assume zero current through inductor L and zero charge across C before closing the switch. 11. Derive an expression for current response of RLC series circuit transient. (16) 29 V.MOHAMED IBRAHIM AP/EEE www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
  • 30. UNIT V THREE PHASE CIRCUITS PART-A 1. Define line current and phase current. The current flowing through the line is called line current The current flowing through the phase is called phase current 2. Define line and phase voltag The voltage between two lines is called the line voltage The voltage between any line and the neutral point is called phase voltage. 3. Give the line and phase values in star connection The relation between line and phase voltage in star connection is EL=√3Eph The relation between line current and phase current in a star connection is IL=Iph 4. Give the line and phase values in delta connection The relation between line voltage and phase voltage in a delta connection is EL=Eph The relation between line current and phase current in delta connection is IL=√3Iph 30 V.MOHAMED IBRAHIM AP/EEE www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
  • 31. 5. Write few methods available for measuring in 3-phase load. One wattmeter method Two wattmeter method Three wattmeter method 6. List the methods used for power measurement with single wattmeter Potential lead shift method T- method Artificial neutral method Current transformer method 7. List the methods for unbalanced star connected load Equivalents delta method Mesh method Neutral voltage displacement method 8. Write the methods of conne ctions of 3 phase windings? Independent connection Star connection and Delta connection 31 V.MOHAMED IBRAHIM AP/EEE www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com
  • 32. PART – B 1. With a neat circuit and phasor diagram explain the three phase power measurement by two wattmeter methods. 2. (i) A symmetrical three phase 400V system supplies a balanced delta connected load. The current in each branch circuit is 20A and phase angle 40° (lag) calculate the line current and total power. (8) (ii) A three phase delta connected load has Zab = (100+j0) ohms, Zbc = (-j100) ohms and Zca = (70.7 =j70.7) ohms is connected to a balanced 3 phase 400V supply. Determine the line currents Ia,Ib and Ic. Assume the phase sequence abc. (8) 3. (i) A balanced three phase star connected load with impedance 8+j6 ohm per phase is connected across a symmetrical 400V three phase 50Hz supply. Determine the line current, power factor of the load and total power. (8) (ii) An alternating current is expressed as i=14.14 sin 314t. Determine rms current, frequency and instantaneous current hen t =0.02ms. (8) 4. (i) A balanced star connected load of 4+j3 ohm per phase is connected to a 400V, 3 phase, 50Hz supply. Find the line current, power factor, power, reactive volt ampere and total volt ampere. (8) (ii) A Voltage source 100V with resistance of 10 ohms and inductance 50 mH, a capacitor 50 microfarad are connected in series. Calculate the impedance when the frequency is (i) 50HZ (ii) 500Hz (iii) the power factor at 100Hz. (8) 5. (i) Three impedances Z1 = 3∟45° ohm, Z2 = 10 √2∟45° ohm, Z3 = 5 ∟-90° ohm are connected in series. Calculate applied voltage if voltage across Z1 = 27∟-10° V. (8) (ii) A delta connected load as shown in figure is connected across 3 phase 100 volt supply. Determine all line currents. (8) 32 V.MOHAMED IBRAHIM AP/EEE www.Vidyarthiplus.comwww.Vidyarthiplus.comwww.Vidyarthiplus.com