Question

There are two metallic wires of same material, same length but of different radii. When these are connected to an ideal battery in series, heat produced is $H_1$ but when connected in parallel, heat produced is $H_2$ for the same time. Then the correct statement is

• A. $H_1=H_2$
• B. $H_1<H_2$
• C. $H_1>H_2$
• D. No relation

Answer 1

The correct option is B $H_1<H_2$

When wire are in series $R_{eq/Series}=R_1+R_2$

$H_1$=$V^2/R_{eq/Series}$

In case of parallel $\frac{1}{R_{eq/Parallel}}=\frac{1}{R_1}$ + $\frac{1}{R_2}$

$H_2=V^2/R_{eq/Parallel}$

As $R_{eq/Series}$ is greater then $R_{eq/parallel}$

Hence $H_1$<$H_2$