Question

Two conducting wires of the same material and of equal lengths and equal diameters are first connected in series and then in parallel in a circuit across the same potential difference. The ratio of heat produced in series and parallel combinations would be :

• A. 1:2
• B. 2:1
• C. 1:4
• D. 4:1

Answer 1

Answer: (C)

1:4

Since the two wires have same material, length and diameter, they have the same resistance. Let the resistance of each wire be R.

Let applied potential difference be $V$.

$R_{series}=R_1+R_2$

$=R+R=2R$

$P_{series}=V^2/R_{series}$

$=V^2/\left(2R\right)..........\left(i\right)$

$\frac{1}{R_{parallel}}=\frac{1}{R_1}+\frac{1}{R_2}$

$R_{parallel}=R/2$

$P_{parallel}=V^2/R_{parallel}$

$=2V^2/R............\left(ii\right)$

Dividing (ii) from (i),

$\frac{P_{series}}{P_{parallel}}=1/4$