Question

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

• A. 1:4
• B. 4:1
• C. 2:1
• D. 1:2

Answer 1

The correct option is A 1:4

Heat produced in the circuit is inversely proportional to the resistance R.
Let $R_s$ be the equivalent resistances of the wires if connected in series and $R_p$ be the equivalent resistances of the wires if connected in parallel.
$R_s=R+R=2R$ and $\frac{1}{R_p}=\frac{1}{R}+\frac{1}{R}$
$\frac{1}{R_p}=\frac{2}{R}$ or $R_p=\frac{R}{2}$
In both the cases, potential difference is same $V$ and the time taken is $t$.
Now, the ratio of heat produced is given by
$\frac{H_s}{H_p}=\frac{\frac{V^2}{R_s}t}{\frac{V^2}{R_p}t}$
$=\frac{R_p}{R_s}$
$=\frac{\frac{R}{2}}{2R}$
$=\frac{1}{4}$