Q. In the following circuit, $18\Omega$ resistor develops $2J/sec$ due to current flowing through it. The power developed across $10\Omega$ resistance is
A) $125\ W$
B) $10\ W$
C) $\frac{4}{5}W$
D) $25\ W$
Explanation
(b) The given circuit can be redrawn as
$\frac{i_{1}}{i_{2}} = \frac{9}{18} = \frac{1}{2}$
and $i = i_{1} + i_{2}$
$\Rightarrow \frac{i}{i_{1}} = 1 + \frac{i_{2}}{i_{1}} = 1 + 2 = 3$
From $P = i^{2}R \Rightarrow \frac{P_{10\Omega}}{P_{18\Omega}} = \left( \frac{i}{i_{1}} \right)^{2} \times \frac{10}{18} \Rightarrow P_{10\Omega} = 10W$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.