Question

Figure shows three resistor configurations $R1,R2$ and $R3$ connected to $3V$ battery. If the power dissipated by the configuration $R1,R2$ and $R3$ is $P1,P2$ and $P3$, respectively, then

• A. $P1>P2>P3$
• B. $P1>P3>P2$
• C. $P2>P1>P3$
• D. $P3>P2>P1$

Answer 1

The correct option is C $P2>P1>P3$

For $R_1$: This is a equivalent wheatstone bridge circuit. The equivalent

resistance $R_1=R=1\Omega$.

For $R_2$: The equivalent resistance $R_2={(\frac{1}{1+1}+1+\frac{1}{1+1})}^{-1}=2^{-1}=0.5\Omega$

For $R_3$: The equivalent resistance $R_3=1+\frac{(1+1)(1+1)}{(1+1)+(1+1)}=1+1=2\Omega$

As $P=\frac{V^2}{R}$ and $V=3$ for each so $P\propto \frac{1}{R}$

Thus, $P_2>P_1>P_3$