Question

Two resistances $R$ and $2R$ are connected in parallel in an electric circuit. The thermal energy developed in $R$ and $2R$ are in the ratio

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

Answer 1

Answer: (B)

Given that, the two resistance $R$ and $2R$ are connected in parallel so the potential drop are equal for both
The thermal energy developed in a circuit is
$H=\frac{V^{2}t}{R}$
$\Rightarrow H\propto \frac{1}{R}$
$\Rightarrow \frac{H_1}{H_2}=\frac{R_2}{R_1}$
$\Rightarrow \frac{H_1}{H_2}=\frac{2R}{R}$
[Here, $R_1=R,R_2=2R$]
or $H_1:H_2=2:1$
Hence, the correct answer is $(b)$