Q. Figure shows three resistor configurations $R_{1},\ R_{2}\ and\ R_{3}$ connected to 3 V batteries. If the power dissipated by the configuration $R_{1},\ R_{2}\ and\ R_{3}$ IS $P_{1},\ P_{2}\ and\ P_{3},$ respectively, then
A) $P_{1} > P_{2} > P_{3}$
B) $P_{1} > P_{3} > P_{2}$
C) $P_{2} > P_{1} > P_{3}$
D) $P_{3} > P_{2} > P_{1}$
Explanation
(c) Applying $\ \ \ \ \ \ \ \ \ \ \ P = \frac{V^{2}}{R}$
$R_{1} = 1\ \Omega,\ R_{2} = 0.5\ \Omega\ and\ R_{3} = 2\ \Omega,\ V_{1} = V_{2} = V_{3} = 3\ volt$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ P_{1} = \frac{(3)^{2}}{1} = 9\ W$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ P_{2} = \frac{(3)^{2}}{0.5} = 18\ W\ and$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ P_{3} = \frac{(3)^{2}}{2} = 4.5\ W$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ P_{2} > P_{1} > P_{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.