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Question

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


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

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

Physics
NCERT
Standard XII

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