1. electronics fundamentals
circuits, devices, and applications
THOMAS L. FLOYD
DAVID M. BUCHLA
Chapter 5 – Parallel Circuits

2. Resistors that are connected to the same two points are said to be in parallel.

3. A parallel circuit occurs if:
more than one current path (branch) is connected to a common voltage source.
The voltage between the two points appears across each of the branches.

9. Draw the parallel circuits shown below as schematics

10. Connect the groups of resistors to make parallel circuits.

12. Connecting resistors in parallel
reduces total resistance and
increases total current.
60 amp
120 amp
24 v
24 v

13. From Chapter 2, what is Conductance and its unit
Conductance (C) is:
ease with which current can pass
the reciprocal of resistance,
Siemens

14. Parallel circuit rule for resistance
The total resistance of resistors in parallel is
the reciprocal of the sum of the reciprocals of the individual resistors.
For example, the resistors in a parallel circuit are 680 W, 1.5 kW, and 2.2 kW. What is the total resistance?
386 W

15. The total resistance of resistors in parallel is
the reciprocal of the sum of the reciprocals of the individual resistors.
GT = G1 + G2 + G3 + … + GN

16. What is RT (REQuivalent) for this circuit
200
3500 50
RT = ohms

17. Special formula for calculating resistance of two parallel resistors
The resistance of two parallel resistors can be found by
either: or
Total resistance of two resistors in parallel is equal the product of the two resistors divided by the total resistance.
What is the total resistance if R1 = 27 kW and R2 = 56 kW?
18.2 kW

18. Special formula for calculating resistance for equal resistors in parallel
500
500
500
500
500
What is the value of RT
100 ohms

19. Special formula for calculating resistance for equal resistors in parallel
500
500
500
500
100
What is the value of RT
55.56 ohms

20. Application of a parallel circuit for the exterior light system of an automobile.
What happens if one headlight burns out?
What happens to the current drawn by the headlight circuit?

21. Parallel circuits are used in residential wiring.
WHY?

22. Draw the schematic for this circuit board.

23. Voltage across parallel branches is the same.
Parallel circuit rule for voltage
Voltage across parallel branches is the same.

24. Parallel circuit rule for voltage
Because all components are connected across the same voltage source, the voltage across each is the same.
The source voltage is 5.0 V. What will a volt- meter read if it is placed across each of the resistors?

26. 24 v
What is the voltage reading for R1 and R2

27. What is the voltage reading for R1 and R2

28. Application of Ohms law
Calculate VS, I1, I2 and I3.
Calculate IS if R3 is shorted, if R3 is open and voltage remains the same
Vs = volts, RT = ohms, I1=0.023a, I2=0.009a, I3=.00505a
Ishort = Error; RT = 158 ohms, IS = 32mA

29. Kirchhoff’s current law (KCL)
The sum of the currents into a node equals the sum of the current out of that node.

30. Kirchhoff’s current law (KCL)
The algebraic sum of the currents entering and leaving a node equals zero.

31. Proving Kirchhoff’s current law.

32. Parallel circuits are know as current “dividers”

33. Parallel Circuit is a Current divider
When current enters a node (junction)
it divides into currents with values that are inversely proportional to the resistance values.

34. The current IX through any branch equals
The total parallel resistance RT
Divided by the resistance RX for that branch
Multiplied by
The total current IT in the branch

35. Current divider For two resistor parallel circuits and
Notice the subscripts. The resistor in the numerator is not the same as the one for which current is found.

36. The branch with the lowest resistance has the most current, The branch with the highest resistance has the least current.

37. Current divider

38. Solving for Current in a parallel circuit when the voltage is unknown and the IT and the values of R1 and R2 are known.

39. Current divider
Assume that R1is a 2.2 kW resistor that is in parallel with R2, which is 4.7 kW. If the total current into the resistors is 8.0 mA, what is the current in each resistor?
5.45 mA
2.55 mA
Notice that the larger resistor has the smaller current.

40. Power in parallel circuits
Power in each resistor can be calculated with any of the standard power formulas.
Just like a series circuit
PT = P1 + P2 + P3 + … + PN
What is the total power if 10 V is applied to the parallel combination of R1 = 270 W and R2 = 150 W?
1.04 W

41. What is the maximum power that the amplifier must be able to deliver?
Power for one speaker = watts

42. Assume there are 8 resistive wires all with the same resistance that form a rear window defroster for an automobile.
(a) If the defroster dissipates 90 W when connected to a 12.6 V source, what power is dissipated by each resistive wire?
(b) What is the total resistance of the defroster?
(a) Each of the 8 wires will dissipate 1/8 of the total power
(b) The total resistance is
1.76 W x 8 = 14.1 W
What is the resistance of each wire?

43. When an open condition occurs in a parallel circuit:
Open branches in parallel circuits
When an open condition occurs in a parallel circuit:
the total resistance increases and
the total current decreases and
the current through all other branches (i.e. R2) remains unchanged.

44. When a lamp filament opens (or the light is turned off), the total current decreases by the amount of current in the lamp that opened. The other branch currents remain unchanged.

45. Finding an open path by current measurement.
Troubleshooting parallel circuits
Finding an open path by current measurement.

46. Know how to determine if there is a open resistor
Troubleshooting parallel circuits
Know how to determine if there is a open resistor

47. Practice Exercise Complete the parameters listed in the Table.
I1= R1= 0.68 kW V1= P1=
I2= R2= 1.50 kW V2= P2=
I3= R3= 2.20 kW V3= P3=
IT= RT= 386 W VS= 5.0 V PT=
7.4 mA
5.0 V
36.8 mW
3.3 mA
5.0 V
16.7 mW
2.3 mA
5.0 V
11.4 mW
13.0 mA
64.8 mW

48. Key Terms
The relationship in electric circuits in which two or more current paths are connected between two separate points (nodes).
Parallel
Branch
Kirchhoff’s current law
Node
Current divider
One current path in a parallel circuit.
A law stating the total current into a node equals the total current out of the node.
A point or junction in a circuit at which two or more components are connected.
A parallel circuit in which the currents divide inversely proportional to the parallel branch resistances.

49. 1. The total resistance of parallel resistors is equal to
a. the sum of the resistances
b. the sum of the reciprocals of the resistances
c. the sum of the conductances
d. none of the above

50. Quiz 2. The number of nodes in a parallel circuit is a. one b. two
c. three
d. any number

51. 3. The total resistance of the parallel resistors is
a kW
b kW
c. 5.1 kW
d kW

52. 4. If three equal resistors are in parallel, the total resistance is
a. one third the value of one resistor.
b. the same as one resistor.
c. three times the value of one resistor.
d. the product of the three resistors

53. Quiz 5. In any circuit the total current entering a node is
a. less than the total current leaving the node.
b. equal to the total current leaving the node.
c. greater than the total current leaving the node.
d. can be any of the above, depending on the circuit.

54. 6. The current divider formula to find I1 for the special case of two resistors isb. c. d.

55. 7. The total current leaving the source is
a. 1.0 mA
b. 1.2 mA
c. 6.0 mA
d. 7.2 mA

56. 8. The current in R1 is
a. 6.7 mA
b mA
c. 20 mA
d mA

57. 9. The voltage across R2 is
a. 0 V
b V
c V
d. 4.0 V

58. 10. The total power dissipated in a parallel circuit is equal to the
a. power in the largest resistor.
b. power in the smallest resistor.
c. average of the power in all resistors.
d. sum of the power in all resistors.

59. Quiz
Answers:
1. d
2. b
3. a
4. a
5. b
6. c
7. d
8. b
9. c
10. d