Question

Two resistances 20 W and 40 W are connected in series to a battery of potential difference 10 Volt compare the ratio of the heat produced in one minute in the two resistances.

Answer 1

Step 1: Heat in terms of power and time,

Write the formula for the heat produced.

$H=I^{2}Rt$ …….. (1)

Here, I is current, R is the resistance and t is the time.

Write the formula for the power.

$P=I^{2}R$

Substitute the above equation in equation (1).

$H=Pt$ ……. (2)

Step 2: Calculate the ratio,

Consider the power consumed in two resistors are $P_1$and $P_2$ and the respective heat produced by them is $H_1$and $H_2$.

Then, from equation (1) the ratio is,

$\frac{H_1}{H_2}=\frac{P_{1}t}{P_{2}t}$

Since time is both for the same that is 1 minute.

$\begin{array}{rcl}\frac{H_1}{H_2}& =& \frac{P_1}{P_2}\\ & =& \frac{20\mathrm{W}}{40\mathrm{W}}\\ & =& \frac{1}{2}\end{array}$

Therefore, the ratio of the heat produced in 1 minute is 1:2.