In the circuit diagram given in Fig. 12.10, suppose the resistors R
1
,R
2
and R
3
have the values 5 Ω, 10 Ω, 30 Ω, respectively, which havebeen connected to a battery of 12 V. Calculate
(a) the current through each resistor,
(b) the total current in the circuit, and
(c) the total circuit resistance.
Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Example 12.8 In the circuit diagram given in Fig. 12.10, suppose the resistors R1, R2 and R3 have the values 5 Ω, 10 Ω, 30 Ω, respectively, which have been connected to a battery of 12 V. Calculate (a) the current through each resistor, (b) the total current in the circuit, and (c) the total circuit resistance.
Given,
R1 = 5 Ω
R2 = 10 Ω
R3 = 30 Ω
Potential difference = V = 12 V
We know that,
in a parallel connection
The potential difference across each resistor is same.
The current across each resistor is different
By ohm’s law,
V = I R
𝑉/𝑅 = I
I = 𝑉/𝑅
Finding current through each resistor
R1 = 5 Ω
I1 = 𝑉/𝑅_1
= 12/5
= 2.4 A
R2 = 10 Ω
I2 = 𝑉/𝑅_2
= 12/10
= 1.2 A
R3 = 30 Ω
I3 = 𝑉/𝑅_3
= 12/30
= 0.4 A
(b) Total current in the circuit
In parallel connection,
Total current through the circuit
= Sum of current through each resistor
= I1 + I2 + I3
= 2.4 + 1.2 + 0.4
= 4A
(c) Total circuit resistance
In parallel connection,
Total resistance is given by
1/𝑅 = 1/𝑅_1 + 1/𝑅_2 + 1/𝑅_3
1/𝑅 = 1/5 + 1/10 + 1/30
1/𝑅 = (6 + 3 + 1)/30
1/𝑅 = 10/30
R = 30/10
R = 3 Ω
Thus,
Current through each resistor
I1 = 2.4 A
I2 = 1.2 A
I3 = 0.4 A
(b) Total current is 4 A
(c) Total Resistance = 3 Ω
CA Maninder Singh is a Chartered Accountant for the past 13 years and a teacher from the past 17 years. He teaches Science, Economics, Accounting and English at Teachoo
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