Question

In the circuit shown, the thermal power dissipated in $R_1$ is $P$. The thermal power dissipated in $R_2$ is

• A. $P$
• B. $\frac{4P}{9}$
• C. $\frac{2P}{3}$
• D. $\frac{P}{9}$

Answer 1

The correct option is B $\frac{4P}{9}$

Consider the problem

Current $i$ divides in two branches and the two are parallel, then the

voltage across them are same

And current divides in $i_1$ and $i_2$

Therefore,

$i_1\times R=i_2\times 2R$

$i_1=2i_2$ ---- (i)

And

$i=i_1+i_2=1$

then, from (i)

$i_1=\frac{2}{3}i$

Power in $R_1,P=i^{2}R$

And

Power in $R_2=\frac{4}{9}{i}^{2}R=\frac{4P}{9}$

Hence, option $B$ is the correct answer which is is $\frac{4P}{9}$