Question

Resistance of conductor is doubled keeping the potential difference across it constant. The rate of generation of heat will:

• A. become one fourth
• B. be halved
• C. be doubled
• D. become four times

Answer 1

The correct option is B be halved

We know that heat generated in a current carrying conductor is expressed as:
$H=I^{2}Rt$
Now, $V=IR\Rightarrow I=\frac{V}{R}$
So, $H=\frac{V^2}{R^2}\times R\times t$
or, $H=\frac{V^2.t}{R}$
or, $\frac{H}{t}=\frac{V^2}{t}=$ rate of heat generation
Now, as par given condition, $V$ remains unchanged.
So, $\frac{H}{t}\propto \frac{1}{R}$
This means, when resistance is doubled, rate of heat generation will be halved.