Question

A current is passed through a resistor for some time. It produces 400 cal of heat in this period. If the current is doubled, how much heat (in calories) will be produced for the same duration?

Answer 1

heat produced when a current i is passed through a resistor of resistance R for time t is given by H = i²Rt

If R and t are constants. H is directly proportional to i².

so, $\frac{H_1}{H_2}=\frac{i_1^2}{i_2^2}$

given, $H_1=400Cal$ , $i_2=2i_1$

now, $\frac{400Cal}{H_2}=\frac{i_1^2}{(2i_1)^2}$

or, $\frac{400Cal}{H_2}=\frac{1}{4}$

or, $H_2=1600Cal$

hence, if the current is doubled, 1600Cal heat will be produced for the same duration.

Answer 2

$\huge \bf \: \frac{H_1}{H_2}=\frac{i_1^2}{i_2^2}$

$\huge \bf \: \frac{400Cal}{H_2}=\frac{i_1^2}{(2i_1)^2}$

$\huge \bf \frac{400Cal}{H_2}=\frac{1}{4}$

=1600Cal