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Basics of Electrical Engineering
AC and DC meters
Kirchhoff's Laws

By
Ms. Nishkam Dhiman
Assistant Professor -EEE Deptt.
Chitkara Institute of Engg. & Technology
Types of instruments used as
ammeters and voltmeters
PMMC(permanent magnet moving coil) (Only D.C.)
Moving Iron
Electrodynamometer
Electrostatic
Thermocouple
Induction (only A.C)
DC Meter
PMMC
The Permanent Magnet Moving Coil (PMMC)

galvanometer used for dc measurement only.
The motor action is produced by the flow of a small
current throught a moving coil which is positioned in
the field of a permanent magnet
The basic moving coil system-D’Arsonval
galvonometer
d’Arsonval meter(PMMC)
Deflecting Torque
Resulting from the effects of magnetic electrostatic.
This torque causes the pointer moves from the zero

position
Deflecting Torque
Td = BANI (Nm)
B=
N=
A=
I =

flux density in Wb/m2 or Tesla (T)
number of coils
Area cross-section
(length (l) x coil diameter (d)m2 )
current flowing through the coil - Ampere
Damping Torque
The torque which makes the pointer to come to a

steady position without overshooting.
Air friction damping
Fluid friction damping
Eddy current damping
Electromagnetic damping
DC VOLTMETER
The basic d’Arsonval meter can be converted to a dc

voltmeter by connecting a multiplier Rs in series with
it as shown in Figure . The purpose of the multiplier is
to extend the range of the meter and to limit the
current through the d’Arsonval meter to the
maximum full-scale deflection current.
Ac Meters

AC electromechanical meter movements come in two

basic arrangements:
those based on DC movement designs,
and those engineered specifically for AC use. (measure
RMS value)
Permanent-magnet moving coil (PMMC) meter movements
will not work correctly if directly
connected to alternating current
because the direction of needle
movement will change with
each half-cycle of the AC.
In order to use a DC-style meter movement such as the

D'Arsonval design, the alternating current must
be rectified into DC. This is most easily accomplished
through the use of devices called diodes.
Moving Iron
The simplest design is to use a non magnetized iron vane

to move the needle against spring tension, the vane being
attracted toward a stationary coil of wire energized by the
AC quantity to be measured as in Figure
AC measurements are often cast in a scale of DC power

equivalence, called RMS (Root-Mean-Square) for the sake
of meaningful comparisons with DC and with other AC
waveforms of varying shape. Meter movements relying on
the motion of a mechanical needle (“rectified” D'Arsonval,
iron-vane, and electrostatic) all tend to mechanically
average the instantaneous values into an overall average
value for the waveform. This average value is not
necessarily the same as RMS, although many times it is
mistaken as such. Average and RMS values rate against each
other as such for these three common waveform shapes:
(Figure below)
RMS an Average Values
Electrodynamometer
The working principle of a basic electrodynamometer

instrument is same as the PMMC instrument.
 The only difference in this case is that the permanent
magnet is replaced with two fixed coils connected in
series.
The moving coil is also connected in series with the fixed
coils. The two fixed coils are connected to electromagnets
in such a manner that they form poles of opposite polarity.
As the moving coil carries current through it and is being
placed in the field of fixed coils, it experience a force due
to which the moving coil rotates.
Electrodynamometer
Thermocouple Type :
One answer is to design the meter movement around the
very definition of RMS: the effective heating value of an AC
voltage/current as it powers a resistive load. Suppose that
the AC source to be measured is connected across a resistor
of known value, and the heat output of that resistor is
measured with a device like a thermocouple. This would
provide a far more direct measurement means of RMS than
any conversion factor could, for it will work with ANY
waveform shape whatsoever: (Figure below)
Identification of AC and DC
meters
DC meters are have uniform Scale where as AC

meters are non-uniform Scale.
As the force acting on pointer is directly proportional
to current in DC and square of the current in AC. In
the beginning the graduations are cramped and
afterwards ,they go on becoming wider and wider.
Resistance and Laws of Resistance
Electrical resistance may be defined as the basic property of

any substance due to which it opposes the flow of electric
current through it
The laws of resistance state that,
electrical resistance R of a conductor or wire is
1) directly proportional to its length, l i.e. R ∝ l
2) inversely proportional to its area of cross - section, a i.e.
3)depends upon nature of material
4)Depends on the temperature of the conductor.
Combining these first two laws we get, R= ρ.l/a
Where ρ (rho) is the proportionality constant and known

as resistivity or specific resistance of the material of the
conductor or wire. Now if we put, l = 1m and a = 1square
meter in the equation,
We get, R = ρ. That means resistance of a material of unit
length having unit cross - sectional area is equal to
its resistivity or specific resistance.
Units of resistivity
The unit of resistivity can be easily determined form its equation
ohm-m
Kirchhoff’s Current Law
At any junction point in an electrical circuit, the total

current into the junction equals the total current out of the
junction.
(“What goes in must come out.”)
In the diagram at right,
I1 + I2 = I3
OR

N

∑i
n =1

n

=0
Where N is the total number of
branches connected to a node.

∑i

enter

node

=

∑i

leave

node
Example 1 (KCL)
Determine I, the current flowing out of the voltage

source.

Use KCL

1.9 mA + 0.5 mA + I are
entering the node.
 3 mA is leaving the node.


1.9mA + 0.5mA + I = 3mA
I = 3mA − (1.9mA + 0.5mA)
I = 0.6mA
V1 is generating power.
Kirchhoff’s Voltage Law
In any complete path in an electrical circuit, the sum of

the potential increases equals the sum of the potential
drops.
(“What goes up must come down.”)
M

∑

v= 0

m =1

Where M is the total number of branches
in the loop.

∑

v drops = ∑ v rises
Example 2 (KVL)
Find the voltage across R1. Note that the polarity of the

voltage has been assigned in the circuit schematic.
First, define a loop that include R1.
Example 2 (con’t)
If the outer loop is used:
Follow the loop clockwise.
Example 2 (con’t)
By convention, voltage drops are added and voltage

rises are subtracted in KVL.

− 5V − VR1 + 3V = 0
VR1 = 2V
Summary
The currents at a node can be calculated using

Kirchhoff’s Current Law (KCL).
The voltage dropped across components can be
calculated using Kirchhoff’s Voltage Law (KVL).
Ohm’s Law is used to find some of the needed
currents and voltages to solve the problems.
Wheatstone Bridge
A Wheatstone bridge is an electrical circuit used to 

measure an unknown electrical resistance by balancing 
two legs of a bridge circuit, one leg of which includes the 
unknown component. Its operation is similar to the 
original potentiometer.
In the above figure, Rx is the unknown resistance to

be measured; , and R1,R2 and R3 are resistors of known
resistance and the resistance of Rx is adjustable. If the
ratio of the two resistances in the known leg R2/R1 is
equal to the ratio of the two in the unknown leg
Rx/R3 , then the voltage between the two midpoints
(B and D) will be zero and no current will flow through
the galvanometer . If the bridge is unbalanced, the
direction of the current indicates whether R2 is too
high or too low. R2 is varied until there is no current
through the galvanometer, which then reads zero.
At the point of balance, the ratio of

R2/R1 = Rx/R3
Rx = R2.R3/R1
Applications
(1) to measure the value of an unknown resistor by
comparison to standard resistors, and
(2) to detect small changes in a resistance transducer
(e.g. thermistor A thermistor is a type of resistor
whose resistance varies significantly with temperature,
more so than in standard resistors.) The bridge is
initially balanced to "zero the baseline", then any
changes in the transducer's resistance (R3) are detected
by recording the detector voltage as it varies from zero.
Thanks !

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Ac and dc meters and kirchoff's laws

  • 1. Basics of Electrical Engineering AC and DC meters Kirchhoff's Laws By Ms. Nishkam Dhiman Assistant Professor -EEE Deptt. Chitkara Institute of Engg. & Technology
  • 2. Types of instruments used as ammeters and voltmeters PMMC(permanent magnet moving coil) (Only D.C.) Moving Iron Electrodynamometer Electrostatic Thermocouple Induction (only A.C)
  • 3. DC Meter PMMC The Permanent Magnet Moving Coil (PMMC) galvanometer used for dc measurement only. The motor action is produced by the flow of a small current throught a moving coil which is positioned in the field of a permanent magnet The basic moving coil system-D’Arsonval galvonometer
  • 5. Deflecting Torque Resulting from the effects of magnetic electrostatic. This torque causes the pointer moves from the zero position
  • 6. Deflecting Torque Td = BANI (Nm) B= N= A= I = flux density in Wb/m2 or Tesla (T) number of coils Area cross-section (length (l) x coil diameter (d)m2 ) current flowing through the coil - Ampere
  • 7. Damping Torque The torque which makes the pointer to come to a steady position without overshooting. Air friction damping Fluid friction damping Eddy current damping Electromagnetic damping
  • 8. DC VOLTMETER The basic d’Arsonval meter can be converted to a dc voltmeter by connecting a multiplier Rs in series with it as shown in Figure . The purpose of the multiplier is to extend the range of the meter and to limit the current through the d’Arsonval meter to the maximum full-scale deflection current.
  • 9. Ac Meters AC electromechanical meter movements come in two basic arrangements: those based on DC movement designs, and those engineered specifically for AC use. (measure RMS value) Permanent-magnet moving coil (PMMC) meter movements will not work correctly if directly connected to alternating current because the direction of needle movement will change with each half-cycle of the AC.
  • 10. In order to use a DC-style meter movement such as the D'Arsonval design, the alternating current must be rectified into DC. This is most easily accomplished through the use of devices called diodes.
  • 11. Moving Iron The simplest design is to use a non magnetized iron vane to move the needle against spring tension, the vane being attracted toward a stationary coil of wire energized by the AC quantity to be measured as in Figure
  • 12. AC measurements are often cast in a scale of DC power equivalence, called RMS (Root-Mean-Square) for the sake of meaningful comparisons with DC and with other AC waveforms of varying shape. Meter movements relying on the motion of a mechanical needle (“rectified” D'Arsonval, iron-vane, and electrostatic) all tend to mechanically average the instantaneous values into an overall average value for the waveform. This average value is not necessarily the same as RMS, although many times it is mistaken as such. Average and RMS values rate against each other as such for these three common waveform shapes: (Figure below)
  • 13. RMS an Average Values
  • 14. Electrodynamometer The working principle of a basic electrodynamometer instrument is same as the PMMC instrument.  The only difference in this case is that the permanent magnet is replaced with two fixed coils connected in series. The moving coil is also connected in series with the fixed coils. The two fixed coils are connected to electromagnets in such a manner that they form poles of opposite polarity. As the moving coil carries current through it and is being placed in the field of fixed coils, it experience a force due to which the moving coil rotates.
  • 16. Thermocouple Type : One answer is to design the meter movement around the very definition of RMS: the effective heating value of an AC voltage/current as it powers a resistive load. Suppose that the AC source to be measured is connected across a resistor of known value, and the heat output of that resistor is measured with a device like a thermocouple. This would provide a far more direct measurement means of RMS than any conversion factor could, for it will work with ANY waveform shape whatsoever: (Figure below)
  • 17. Identification of AC and DC meters DC meters are have uniform Scale where as AC meters are non-uniform Scale. As the force acting on pointer is directly proportional to current in DC and square of the current in AC. In the beginning the graduations are cramped and afterwards ,they go on becoming wider and wider.
  • 18. Resistance and Laws of Resistance Electrical resistance may be defined as the basic property of any substance due to which it opposes the flow of electric current through it The laws of resistance state that, electrical resistance R of a conductor or wire is 1) directly proportional to its length, l i.e. R ∝ l 2) inversely proportional to its area of cross - section, a i.e. 3)depends upon nature of material 4)Depends on the temperature of the conductor.
  • 19. Combining these first two laws we get, R= ρ.l/a Where ρ (rho) is the proportionality constant and known as resistivity or specific resistance of the material of the conductor or wire. Now if we put, l = 1m and a = 1square meter in the equation, We get, R = ρ. That means resistance of a material of unit length having unit cross - sectional area is equal to its resistivity or specific resistance. Units of resistivity The unit of resistivity can be easily determined form its equation ohm-m
  • 20. Kirchhoff’s Current Law At any junction point in an electrical circuit, the total current into the junction equals the total current out of the junction. (“What goes in must come out.”) In the diagram at right, I1 + I2 = I3 OR N ∑i n =1 n =0 Where N is the total number of branches connected to a node. ∑i enter node = ∑i leave node
  • 21. Example 1 (KCL) Determine I, the current flowing out of the voltage source. Use KCL 1.9 mA + 0.5 mA + I are entering the node.  3 mA is leaving the node.  1.9mA + 0.5mA + I = 3mA I = 3mA − (1.9mA + 0.5mA) I = 0.6mA V1 is generating power.
  • 22. Kirchhoff’s Voltage Law In any complete path in an electrical circuit, the sum of the potential increases equals the sum of the potential drops. (“What goes up must come down.”) M ∑ v= 0 m =1 Where M is the total number of branches in the loop. ∑ v drops = ∑ v rises
  • 23. Example 2 (KVL) Find the voltage across R1. Note that the polarity of the voltage has been assigned in the circuit schematic. First, define a loop that include R1.
  • 24. Example 2 (con’t) If the outer loop is used: Follow the loop clockwise.
  • 25. Example 2 (con’t) By convention, voltage drops are added and voltage rises are subtracted in KVL. − 5V − VR1 + 3V = 0 VR1 = 2V
  • 26. Summary The currents at a node can be calculated using Kirchhoff’s Current Law (KCL). The voltage dropped across components can be calculated using Kirchhoff’s Voltage Law (KVL). Ohm’s Law is used to find some of the needed currents and voltages to solve the problems.
  • 28. In the above figure, Rx is the unknown resistance to be measured; , and R1,R2 and R3 are resistors of known resistance and the resistance of Rx is adjustable. If the ratio of the two resistances in the known leg R2/R1 is equal to the ratio of the two in the unknown leg Rx/R3 , then the voltage between the two midpoints (B and D) will be zero and no current will flow through the galvanometer . If the bridge is unbalanced, the direction of the current indicates whether R2 is too high or too low. R2 is varied until there is no current through the galvanometer, which then reads zero.
  • 29. At the point of balance, the ratio of R2/R1 = Rx/R3 Rx = R2.R3/R1 Applications (1) to measure the value of an unknown resistor by comparison to standard resistors, and (2) to detect small changes in a resistance transducer (e.g. thermistor A thermistor is a type of resistor whose resistance varies significantly with temperature, more so than in standard resistors.) The bridge is initially balanced to "zero the baseline", then any changes in the transducer's resistance (R3) are detected by recording the detector voltage as it varies from zero.