Question

The ratio of powers dissipated respectively in $R$ and $3R$, as shown is

• A. $9$
• B. $\frac{27}{4}$
• C. $\frac{4}{9}$
• D. $\frac{4}{27}$

Answer 1

The correct option is D $\frac{4}{27}$


Given:
$R_1=R;R_2=2R;R_3=3R$

Current distribution in the circuit will be

$i_1=\frac{R_2}{R_1+R_2}i=\frac{2R}{3R}i=\frac{2i}{3}$

$i_2=\frac{R_1}{R_1+R_2}i=\frac{R}{3R}i=\frac{i}{3}$

So, ratio of power dissipation in $R_1$ and $R_3$

$\frac{P_1}{P_3}=\frac{i_1^2{R}_1}{i_3^2{R}_3}=\frac{(2i/3{)}^{2}R}{i^2\left(3R\right)}$

$\therefore \frac{P_1}{P_3}=\frac{4}{27}$

Hence, option $\left(D\right)$ is correct.