2. ๏ State and apply Ohmโs Law.
๏ Define power and energy including their units.
๏ Calculate energy and power.
๏ Recognizes series, parallel, series-parallel, wye and delta
connections.
๏ Solve circuits (i.e. find currents and voltages of interest) by combining
resistances in series and parallel.
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
Learning Objectives
At the end of the lesson, the learner is expected to:
3. โข This law applies to electric to electric conduction
through good conductors and may be stated as
follows :
โข โThe ratio of potential difference (V) between any two
points on a conductor to the current (I) flowing
between them, is constant, provided the temperature
of the conductor does not change.โ
After George Simon
Ohm (1787-1854), a
German
mathematician who
in about 1827
formulated the law
known after his
name as Ohmโs
Law.
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
Ohmโs Law
4. where R is the resistance of the conductor between the two points
considered.
โข Put in another way, it simply means that provided R is kept constant,
current is directly proportional to the potential difference across the
ends of a conductor. However, this linear relationship between V and I
does not apply to all non-metallic conductors. For example, for silicon
carbide, the relationship is given by V = KI^m where K and m are
constants and m is less than unity. It also does not apply to non-linear
devices such as Zener diodes and voltage-regulator (VR) tubes.
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
Ohmโs Law
5. 1. A coil of copper wire has resistance of 90 ฮฉ at 20ยฐC and is connected
to a 230-V supply. By how much must the voltage be increased in order
to maintain the current constant if the temperature of the coil rises to
60ยฐC ? Take the temperature coefficient of resistance of copper as
0.00428 from 0ยฐC.
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
Illustrative Problems: ( Instructor actual discussion)
-
6. 2. Three resistors are connected in series across a 12-V battery. The first resistor has a
value of 1 ฮฉ, second has a voltage drop of 4 V and the third has a power dissipation of 12
W. Calculate the value of the circuit current.
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
Illustrative Problems: ( Instructor actual discussion)
7. โข Power (P) - it is the rate of doing work. Its units is watt
(W) which represents 1 joule per second.
1 W = 1 J/s
โข If a force of F newton moves a body with a velocity of ฮฝ
m./s then
Power = F ร ฮฝ , watt
โข If the velocity ฮฝ is in km/s, then
Power = F ร ฮฝ, kilowatt
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
Power and Energy
8. Also, in Calculus Based Physics:
, Watts
At any instant:
, Joules
and
, watt-sec or Joules
Note : W is the energy: t is in seconds and P is in watts.
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
Power and Energy
9. โข Energy (W) - ability of doing electrical work. It is the product of power
obtained and time.
In Electric Circuit,
, watt-sec
Note: P is power, E or V is voltage, I is current, R is resistance and t is time
in sec.
FUNDAMENTALS OF ELECTRICAL CIRCUITS
Ohmโs Law and Resistive Circuit
Power and Energy
10. Important SI Units:
(i) Kilowatt-hour (kWh) and kilocalorie (kcal)
(ii) Miscellaneous Units
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
Power and Energy
11. 1. A de-icing equipment fitted to a radio aerial consists of a length of a
resistance wire so arranged that when a current is passed through it,
parts of the aerial become warm. The resistance wire dissipates 1250
W when 50 V is maintained across its ends. It is connected to a d.c.
supply by 100 metres of this copper wire, each conductor of which has
resistance of 0.006 ฮฉ/m.
Calculate:
(a) the current in the resistance wire
(b) the power lost in the copper connecting wire
(c) the supply voltage required to maintain 50 V across the heater itself.
ILLUSTRATIVE PROBLEMS: ( Instructor actual discussion)
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
12. ILLUSTRATIVE PROBLEMS: ( Instructor actual discussion)
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
13. 2. A factory has a 240-V supply from which the following loads are taken :
Lighting : Three hundred 150-W, four hundred 100 W and five hundred
60-W lamps
Heating : 100 kW
Motors : A total of 44.76 kW (60 b.h.p.) with an average efficiency of 75
percent
Misc. : Various load taking a current of 40 A.
Assuming that the lighting load is on for a period of 4 hours/day, the
heating for 10 hours per day and the remainder for 2 hours/day, calculate
the weekly consumption of the factory in kWh when working on a 5-day
week. What current is taken when the lighting load only is switched on ?
ILLUSTRATIVE PROBLEMS: ( Instructor actual discussion)
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
14. ILLUSTRATIVE PROBLEMS: ( Instructor actual discussion)
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
15. โข When some conductors having resistances R1, R2 and R3 etc. are
joined end-on-end as in figure below, they are said to be connected in
series.
โข Being a series circuit, it should be remembered that:
(i) current is the same through all the three conductors.
Resistances in Series
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
16. (ii) but voltage drop across each is different due to its different
resistance and is given by Ohmโs Law.
(iii) sum of the three voltage drops is equal to the voltage applied across
the three conductors.
where R is the equivalent resistance of the series combination. Also,
Resistances in Series
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
17. โข The main characteristics of a series circuit are :
1. same current flows through all parts of the circuit.
2. different resistors have their individual voltage drops.
3. voltage drops are additive.
4. applied voltage equals the sum of different voltage drops.
5. resistances are additive.
6. powers are additive.
Resistances in Series
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
18. Voltage Divider Rule
โข Since in a series circuit, same current flows through each of the given
resistors, voltage drop varies directly with its resistance.
Total resistance R = R1 + R2 + R3 = 12 ฮฉ
According to Voltage Divider Rule, various
voltage drops are :
Figure of series network
Resistances in Series
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
19. 1. A series circuit consists of three resistors A, B, and C connected to a
120 V source. If the voltage drop across resistor A is 30 volts when
the circuit current is 2A, and Rb = 1.5Rc, Calculate the values of Ra,
Rb, and Rc.
2. The resistors in the voltage-divider circuit shown have a tolerance of ๏ฑ
10%. Find the maximum and minimum value of Vo.
ILLUSTRATIVE PROBLEMS: ( Instructor actual discussion)
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
20. 3. A source supplies 120V to the series combination of a 10 ohm
resistance, an 8 ohm resistance and an unknown resistance Rx. The
voltage across the 8 ohm resistance is 20V. Determine the value of the
unknown resistance.
4. Find the voltage Vo for the circuit shown below: Calculate the power at
380V source. Is the power delivering or absorbed?
ILLUSTRATIVE PROBLEMS: ( Instructor actual discussion)
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
21. ILLUSTRATIVE PROBLEMS: ( Instructor actual discussion)
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
SOLUTION for NUMBER 4 : By voltage division :
๐25 ๐ = 380 ๐ (
25 ๐๐โ๐
25๐๐โ๐+75 ๐๐โ๐
)= 95 V
๐ =
95๐
25 ๐๐โ๐
= 0.0038 A
By voltage division to get Vo:
๐ท๐๐๐๐๐๐๐๐ก ๐๐๐๐ก๐๐๐ ๐๐๐ข๐๐๐ = 25,000 ๐ฅ ๐ = 25,000 ๐ฅ 0.0038 ๐ด = 95๐
๐๐ = 95 ๐ (
60๐พ๐โ๐
60 ๐๐โ๐+40 ๐๐โ๐
) = 57 volts
22. โข Three resistances, as joined in figure below are said to be connected in
parallel.
(i) potential drop across all resistances is the same
(ii) current in each resistor is different and is given by Ohmโs Law.
(iii) the total current is the sum of the three separate currents.
Figure of parallel network
Resistances in Parallel
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
23. โข Now,
โข The main characteristics of a parallel circuit are :
1. same voltage acts across all parts of the circuit
2. different resistors have their individual current.
3. branch currents are additive.
4. conductance's are additive.
5. powers are additive.
Resistances in Parallel
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
24. Division of Current in Parallel Circuit
โข In the figure below, two resistances are joined in parallel across a
voltage V. The current in each branch, as given in Ohmโs law, is :
Figure of parallel network
Resistances in Parallel
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
25. โข Hence, the division of current in the branches of a parallel circuit is
directly proportional to the conductance of the branches or inversely
proportional to their resistances. We may also express the branch
currents in terms of the total circuit current thus :
โข The same approach for 3 or more resistances connected in parallel.
Resistances in Parallel
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
26. 1. Three loads A, B, and C are connected in parallel to a 230 volt source.
Load A takes 9.2 kw. load B takes a current of 60 amp. and load C is a
resistance of 4.6 ohms. Calculate:
(a) the resistances of load A and B,
(b) the total equivalent resistance of the three paralleled loads.
(c) the total current
(d) the total power.
ILLUSTRATIVE PROBLEMS: ( Instructor actual discussion)
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
27. 2. A coil wire having a resistance of 3.84 ohms and carrying a current of
0.15 amp. is in parallel with an unknown resistance through which
there is a current of 1.44 amp. Calculate (a) the unknown resistance
(b) the total equivalent resistance.
3. Given the circuit below. Calculate the following:
(a) total equivalent resistance.
(b) total current.
(c) voltage drop across each section.
(d) current through each resistor.
(e) total power taken by the entire circuit.
ILLUSTRATIVE PROBLEMS: ( Instructor actual discussion)
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
28. Figure for problem 3:
ILLUSTRATIVE PROBLEMS: ( Instructor actual discussion)
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
29. 4. Use current division to find the current io and use voltage division to
find the voltage vo, for the circuit shown below.
ILLUSTRATIVE PROBLEMS: ( Instructor actual discussion)
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
SIMPLIFY THESE RESISTANCES FIRST
33. ILLUSTRATIVE PROBLEMS: ( Instructor actual discussion)
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
SOLUTION :
I1= 7.40 A
Type equation
here.
๐ผ2 =7.40(
10
10+18.861
)
18.861
ohms
I2= 2.564 A
๐ผ2 = 2.564 ๐ด
34. ILLUSTRATIVE PROBLEMS: ( Instructor actual discussion)
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
SOLUTION :
I1= 7.40 A I2= 2.564 A
IO =1.972 A ๐๐=2.564(
80
80+24
) = ๐. ๐๐๐ ๐จ
๐ฃ๐ = 2.564 โ 1.972 โ 30 ๐โ๐๐
๐ฃ๐ = 17.76 ๐๐๐๐ก๐
35. โข Circuits combining series and parallel sections with one source of
supply are treated in as much the same way as simple circuits
arrangements.
Figure of series - parallel network
Series-Parallel
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
36. 1. What is the value of the unknown resistor R in figure below if the voltage
drop across the 500 ฮฉ resistor is 2.5 volts ? All resistances are in ohm.
ILLUSTRATIVE PROBLEMS: ( Instructor actual discussion)
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
37. 2. Calculate the effective resistance of the following combination of
resistances and the voltage drop across each resistance when a P.D. of
60 V is applied between points A and B.
ILLUSTRATIVE PROBLEMS: ( Instructor actual discussion)
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
38. 3. The equivalent resistance between terminals a and b in the figure
below is Rab = 23 ohms. Determine the value of R2.
ILLUSTRATIVE PROBLEMS: ( Instructor actual discussion)
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
39. ILLUSTRATIVE PROBLEMS: ( Instructor actual discussion)
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
SOLUTION for NUMBER 3 :
23 =(
12โ6
12+6
+ ๐ 2) * 80
12 โ 6
12 + 6
+ ๐ 2 + 80
+ 7
R2 = 16 ohms
40. 4. Refer to the circuit shown below. With the switch open, we have v2 =
8V. On the other hand, with the switch closed, we have v2 = 6V.
Determine the values of R2 and RL.
ILLUSTRATIVE PROBLEMS: ( Instructor actual discussion)
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
41. โข Resistors are sometimes interconnected to form rather complex
networks. Due to this, some common rules applicable to simple series
and parallel circuits cannot be used for the calculation of equivalent
resistances, branch currents, and voltage drops.
โ - Y and Y - โ Transformation
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
42. โข Considering the connections of resistors below:
โข โ - Y Transformation:
โ - Y and Y - โ Transformation
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
43. โข For โ - Y Transformation : Each of the resistances in the star is equal
to the product of the resistances of the adjacent arms of the delta
divided by the sum of the three delta resistances.
Y-โ Transformation:
For Y-โ Transformation : Each of the resistances in delta is equal to the
sum of the products of the resistances in the star, taken two at a time,
divided by the resistance in the opposite leg.
โ - Y and Y - โ Transformation
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
44. โข Drawn as a 4 terminal arrangement of components
T and ( Tee and Pi )
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
45. โข 2 of the terminals are connects at one node. The node is a
distributed node in the case of the P network.
T and ( Tee and Pi )
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
46. 1. Referring to the figure in our lecture, the three resistances in a delta-
connected group of resistors are X= 35 ohms, Y = 25 ohms, Z = 40
ohms. Calculate the resistances A, B, and C of the equivalent star.
SOLUTION:
๐ด =
๐๐
100
=
25 ๐ฅ 40
100
= 10 ๐โ๐๐
๐ต =
๐๐
100
=
35 ๐ 40
100
= 14 ๐โ๐๐
๐ถ =
๐๐
100
=
35 ๐ 25
100
= 8.75 ohms
ILLUSTRATIVE PROBLEMS: ( Instructor actual discussion)
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
47. 2. The wiring diagram shown below is known as the Wheatstone Bridge
circuit; when the potential difference between points a and b is zero
the bridge is said to be balanced. For the resistance values given, the
bridge is unbalanced. (a) Calculate the total resistance (b) total current
(c) the current at 110 ๏ resistance.
ILLUSTRATIVE PROBLEMS: ( Instructor actual discussion)
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
49. ILLUSTRATIVE PROBLEMS: ( Instructor actual discussion)
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
SOLUTION:
(b) ๐โ๐ ๐ก๐๐ก๐๐ ๐ถ๐ข๐๐๐๐๐ก ๐๐ ๐ผ =
177.6
59.2
= 3 ๐๐๐
(c) ๐๐ ๐๐๐๐๐ข๐ก๐ ๐กโ๐ ๐๐ข๐๐๐๐๐ก ๐กโ๐๐๐ข๐โ ๐กโ๐ 110 โ ๐โ๐ ๐๐๐ ๐๐ ๐ก๐๐ ๐๐ก ๐ค๐๐๐ ๐๐ ๐๐๐๐ ๐ก ๐๐ ๐๐๐๐๐ ๐ ๐๐๐ฆ ๐ก๐ ๐๐๐๐ ๐กโ๐
potential difference between points a and b. To do this, the currents through the branches of the parallel
Circuit of the figure in (a) must be found. These are:
๐ผ120 ๐๐๐๐ก ๐๐๐๐๐โ =
60
120+60
๐ฅ 3 = 1 amp
๐ผ110 ๐๐๐โ๐ก ๐๐๐๐๐โ =
120
120 + 60
๐ฅ 3 = 2 ๐๐๐
50. ILLUSTRATIVE PROBLEMS: ( Instructor actual discussion)
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
SOLUTION:
The voltage drop across M is 84.8 x 1 = 84.8 volts, and the voltage drop across N is 33.6 x 2 = 67.2 volts. Therefore,
The potential difference between a and b will be
๐ธ๐โ๐ = 84.8 โ 67.2 = 17.6 ๐ฃ๐๐๐ก๐
๐ผ110 =
17.6
110
= 0.16 ๐๐๐
Hence, the current through the 110-ohm resistor is
51. 3. If Ra = 6 ๏, Rb = 9๏ and Rc = 3 ๏. Convert ๏ฐ to tee network.
ILLUSTRATIVE PROBLEMS: ( Instructor actual discussion)
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit
52. ๏Nilsson, James W. 2019. Electric Circuits 11th ed. Amazon [C 621.319 N59
2019(CAL)]
๏Nahvi, Mahmood 2018. Schaum's Outline of Electric Circuits 7th ed. Amazon [C
621.3192 N14 2018(CAL)]
๏Kang, James S. 2018. Electric Circuits (MindTap Course List) 1st ed. Amazon [C
621.3192 K13 2018(CAL)]
๏Bird, John 2014. Electrical Circuit Theory and Technology 6th ed. Amazon [C
621.3192 B53 2014(CAL)]
๏Alexander, Charles 2017. Fundamentals of Electric Circuits 6th ed. Amazon [C
621.3815 A12 2017(CAL)]
References
ELECTRICAL CIRCUITS 1 LECTURE
Ohmโs Law and Resistive Circuit