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

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

Tardigrade Admin · Accepted Answer

We know that heat generated in a current carrying conductor is expressed as:

H = I^{2} Rt

Now,

V = I R \Rightarrow I = \frac{V}{R}

So,

H = \frac{V ^{2}}{R ^{2}} \times R \times t

or,

H = \frac{V ^{2} \cdot 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.

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

become one fourth

be halved

be doubled

become four times