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

Solution

## The correct option is B be halvedWe 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 generationNow, 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.PhysicsNCERTStandard XII

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