question_answer

Power dissipated in given circuit is

A) 12 W

B) 24 W

C) 36 W

D) 72 W

Correct Answer: A

Solution :

Let current distribution is
By loop rule in loops 1 and 2, we have
\[5x-2y+3z=0\]	?(i)
\[2x-4y-9z=0\]	?(ii)

\[\Rightarrow \]\[\frac{x}{30}=\frac{y}{51}=\frac{z}{-16}=k\](let)

\[\Rightarrow \]\[x=30k,\]\[y=51k,\]\[z=-16k\]

If R = equivalent resistance of circuit, then\[V=R\,(x+y)\]

\[\Rightarrow \]\[7x-2z=R\,(x+y)\]

\[\Rightarrow \]\[R=\frac{7x-2z}{x+y}=\frac{7\times 30k-2\,(-16k)}{30k+51k}\]\[\Rightarrow \]\[R=\frac{242}{81}=3\Omega \]

So, power dissipated, \[P=\frac{{{V}^{2}}}{R}=\frac{36}{3}=12W\]