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Apr 12, 2023
Lecturer Name [email protected]
Contact Number
IT2001PAEngineering Essentials (1/2)
Chapter 4 - Resistors in Parallel Circuits
2
Chapter 4 - Resistors in Parallel Circuits
IT2001PA Engineering Essentials (1/2)
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.
3
Chapter 4 - Resistors in Parallel Circuits
IT2001PA Engineering Essentials (1/2)
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.
4
Chapter 4 - Resistors in Parallel Circuits
IT2001PA Engineering Essentials (1/2)
Resistors in Parallel
Resistors are connected in parallel when the same voltage is applied across each resistor.
I
R2
R1
V
I1
I2
Two Resistors are connected in parallel
I1 & I2 are branch currents I
is the total current
5
Chapter 4 - Resistors in Parallel Circuits
IT2001PA Engineering Essentials (1/2)
Some Examples of Parallel Circuits
6
Chapter 4 - Resistors in Parallel Circuits
IT2001PA Engineering Essentials (1/2)
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.
7
Chapter 4 - Resistors in Parallel Circuits
IT2001PA Engineering Essentials (1/2)
Voltage Across Resistors in Parallel
The voltage across each resistor is the same.
I2R2
R3I3
I
I1R1
V
V = V1 = V2 = V3
8
Chapter 4 - Resistors in Parallel Circuits
IT2001PA Engineering Essentials (1/2)
Two Lamps Connected in Parallel
x
supplyvoltage
lamp 1lightsup
lamp 2burned out
If one lamp isburned out , the other lamp is still working.
9
Chapter 4 - Resistors in Parallel Circuits
IT2001PA Engineering Essentials (1/2)
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
10
Chapter 4 - Resistors in Parallel Circuits
IT2001PA Engineering Essentials (1/2)
Current in a Parallel Circuit
I = I1 + I2
Total supply current = sum of branch currents
I2R2
I
I1 R1
V
11
Chapter 4 - Resistors in Parallel Circuits
IT2001PA Engineering Essentials (1/2)
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
12
Chapter 4 - Resistors in Parallel Circuits
IT2001PA Engineering Essentials (1/2)
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:
13
Chapter 4 - Resistors in Parallel Circuits
IT2001PA Engineering Essentials (1/2)
Two Unequal Resistors in Parallel
Effective resistance , R is given by
1R =
1R1
+ 1R2
=R2 + R1
R1 R2
=PRODUCT
SUM
I2R2
I1 R1
R =R1 R2
R2 + R1
14
Chapter 4 - Resistors in Parallel Circuits
IT2001PA Engineering Essentials (1/2)
Three Resistors in Parallel
The reciprocal of the equivalent resistance
equals the sum of the reciprocals of the
branch resistances.
Parallel network Equivalent circuit
1RT
=1R1
+1R2
+1R3
RT
R2
R3
R1
15
Chapter 4 - Resistors in Parallel Circuits
IT2001PA Engineering Essentials (1/2)
Equivalent Resistance
Equivalent or Total resistance is smaller than the lowest individual resistance.
Parallel network Equivalent circuit
R
R2
R3
R1
16
Chapter 4 - Resistors in Parallel Circuits
IT2001PA Engineering Essentials (1/2)
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:
17
Chapter 4 - Resistors in Parallel Circuits
IT2001PA Engineering Essentials (1/2)
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.
18
Chapter 4 - Resistors in Parallel Circuits
IT2001PA Engineering Essentials (1/2)
Example 4-3
Find the potential difference across each resistor and the currents flowing through them.R2 =1
R3 =2
I
R1 =1
I2
I3
I1
10V
I1 = 10 / 1 = 10 AI2 = 10 / 1 = 10 AI3 = 10 / 2 = 5 A
V = 10 V potential across each resistor
19
Chapter 4 - Resistors in Parallel Circuits
IT2001PA Engineering Essentials (1/2)
Example 4-4
Two resistors of 30 and 40 respectively are connected in a parallel. Find the total resistance.
R2
R1
1R =
1R1
+ 1R2
1R =
130
+ 140
1R =
0.0333 + 0.025
1R = 0.0583
R = 17.15
R =R2 + R1
R1 R2
R =30 + 40
30 x 40
R = 17.14
OR
20
Chapter 4 - Resistors in Parallel Circuits
IT2001PA Engineering Essentials (1/2)
Current Divider Rule
I R R
R I
21
2 1
I R R
R I
21
1 2
R1I1
I2 R2
I
R2I2
R1I1I
21
Chapter 4 - Resistors in Parallel Circuits
IT2001PA Engineering Essentials (1/2)
Example 4-5
Find I1 and I2 .25
I2
100 I1
I = 10 A
I R R
R I
21
2 1
I1 = [ 25 / (25 +100) ] x 10 = 2 A
I R R
R I
21
1 2
I2 = [ 100 / (25 +100) ] x 10 = 8 A
22
Chapter 4 - Resistors in Parallel Circuits
IT2001PA Engineering Essentials (1/2)
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