Question

Two resistors whose value are in ratio $2:1$ are connected in parallel with one cell. Then the ratio of power dissipated is

• A. $1:2$
• B. $2:1$
• C. $1:4$
• D. $4:1$

Answer 1

The correct option is A

$1:2$

Power dissipated

1. The power dissipated can be calculated using the following formula.

$P=\frac{V^2}{R}$

Here, $P$ is the power dissipated, $V$ is the voltage, and $R$ is the resistance.

2. Hence, the power is inversely proportional to the resistance and directly proportional to the square of the voltage.

3. Since, the resistors are connected in parallel, the voltage across them will be the same.

Hence, the ratio of power can be written as follows:

$$\begin{gathered} \frac{P_1}{P_2}=\frac{R_2}{R_1} \\ \frac{P_1}{P_2}=\frac{1}{2} \end{gathered}$$

Therefore, the ratio of the power dissipated is $1:2$.

Hence, option (A) is correct.