1. IT2001PA
Engineering Essentials (1/2)
Chapter 4 - Resistors in Parallel Circuits
Lecturer Name
lecturer_email@ite.edu.sg
Aug 16, 2012
Contact Number

2. Chapter 4 - Resistors in Parallel Circuits
Lesson Objectives
Upon completion of this topic, you should be able to:
 Apply Ohm’s Law to calculate voltages, currents and
resistances in a parallel circuit.
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3. Chapter 4 - Resistors in Parallel Circuits
Specific Objectives
 State the characteristics of parallel-connected resistors
 Calculate the current flow, voltage drops across the
various resistors and the total resistance for parallel-
connected resistors.
 Use the current divider rule to calculate the branch
current flowing in a circuit consisting of 2 resistors in
parallel.
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4. Chapter 4 - Resistors in Parallel Circuits
Resistors in Parallel
I1 R1
Two Resistors are
connected in parallel
 Resistors are connected in
I2 R2 parallel when the same voltage
is applied across each resistor.
I
I1 & I2 are branch currents I
V is the total current
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5. Chapter 4 - Resistors in Parallel Circuits
Some Examples of Parallel Circuits
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6. Chapter 4 - Resistors in Parallel Circuits
Voltage Across Resistors in Parallel
 The voltage across any branch of a parallel circuit is
equal to the voltage across any of the other branches
in parallel.
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7. Chapter 4 - Resistors in Parallel Circuits
Voltage Across Resistors in Parallel
I1 R1
The voltage across each resistor is
the same.
I2 R2
I3 R3
V = V1 = V 2 = V 3
I
V
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8. Chapter 4 - Resistors in Parallel Circuits
Two Lamps Connected in Parallel
x
lamp 2
burned out
lamp 1
lights If one lamp is
up burned out , the other
lamp is still working.
supply
voltage
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9. Chapter 4 - Resistors in Parallel Circuits
Example 4-1
Determine the voltage
across each resistor in the
figure
Solution:
The five resistors are in parallel, so the voltage drop
across each one is equal to the applied source voltage.
There is no voltage drop across the fuse
V1= V2 = V3 = V4 = V5 =25V
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10. Chapter 4 - Resistors in Parallel Circuits
Current in a Parallel Circuit
I1 R1
I2 R2 I = I 1 + I2
I
V
Total supply current = sum of branch currents
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11. Chapter 4 - Resistors in Parallel Circuits
Example 4-2
The branch currents in the
circuit of the figure are
known. Determine the total
current IT.
Solution
The total current IT is the sum of the two branch
currents.
So the total current into point A is
IT=I1+I2=5mA + 12mA = 17mA
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12. Chapter 4 - Resistors in Parallel Circuits
Total Parallel Resistance
 When resistors are connected in parallel, the total resistance of
the circuit decreases. The total resistance of a parallel circuit is
always less than the value of the smallest resistor.
 The circuit in the figure shows a general case of ‘n’ resistors in
parallel.
 Applying Ohm's Law to the circuit, the total resistance is given by
the equation:
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13. Chapter 4 - Resistors in Parallel Circuits
Two Unequal Resistors in Parallel
I1 R1 Effective resistance , R is
given by
I2 R2
1 1 + 1
=
R R1 R2
R2 + R1
=
R1 R2
R1 R2 PRODUCT
R = =
R2 + R1 SUM
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14. Chapter 4 - Resistors in Parallel Circuits
Three Resistors in Parallel
Parallel network Equivalent circuit
R1 RT
R2
R3
The reciprocal of the equivalent resistance
equals the sum of the reciprocals of the
branch resistances. 1 1 1 1
= + +
RT R1 R2 R3
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15. Chapter 4 - Resistors in Parallel Circuits
Equivalent Resistance
Parallel network Equivalent circuit
R1
R
R2
R3
Equivalent or Total resistance is smaller
than the lowest individual resistance.
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16. Chapter 4 - Resistors in Parallel Circuits
Equal-Value Resistors in Parallel
 Another special case of parallel circuits is the parallel
connection of several resistors having the same
resistance value.
 Suppose there are ‘n’ number of resistors R1, R2, R3,
…….Rn, all with equal resistance value of R each.
 Then total resistance is given by:
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17. Chapter 4 - Resistors in Parallel Circuits
Characteristics of Parallel Circuit
 The voltage across each resistor is the same.
 Total current = Sum of individual current
 The reciprocal of the total resistance = sum of the
reciprocal of each resistance
 Total resistance is smaller than the lowest individual
resistance.
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18. Chapter 4 - Resistors in Parallel Circuits
Example 4-3
I1 R1 =1Ω Find the potential difference across each
resistor and the currents flowing through
I2 R2 =1Ω them.
V = 10 V potential across each resistor
I3 R3 =2Ω
I1 = 10 / 1 = 10 A
I I2 = 10 / 1 = 10 A
I3 = 10 / 2 = 5 A
10V
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19. Chapter 4 - Resistors in Parallel Circuits
Example 4-4
Two resistors of 30Ω and 40Ω respectively are
connected in a parallel. Find the total resistance.
1 1 + 1 OR
=
R R1 R2
R1 R1 R2
1 1 + 1 R =
=
R 30 40 R2 + R1
R2 1
= 0.0333 + 0.025 30 x 40
R R =
1 30 + 40
= 0.0583
R
R = 17.14 Ω
R = 17.15 Ω
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20. Chapter 4 - Resistors in Parallel Circuits
Current Divider Rule
I1 R1
I
R2
I1 = I
I2 R2 R1 + R2
I1 R1
I R1
I2 = I
R1 + R2
I2 R2
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21. Chapter 4 - Resistors in Parallel Circuits
Example 4-5
I1 100 Ω
I = 10 A
25 Ω Find I1 and I2 .
I2
R2
I1 = I I1 = [ 25 / (25 +100) ] x 10 = 2 A
R1 + R2
R1
I2 = I I2 = [ 100 / (25 +100) ] x 10 = 8 A
R1 + R2
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22. Chapter 4 - Resistors in Parallel Circuits
Next Lesson
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