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

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

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.