Q. A capacitor $4\ \mu F$ charged to $50\ V$ is connected to another capacitor of $2\mu F$ charged to $100\ V$ with plates of like charges connected together. The total energy before and after connection in multiples of $\left( 10^{- 2}\ J \right)$ is
A) 1.5 and 1.33
B) 1.33 and 1.5
C) 3.0 and 2.67
D) 2.67 and 3.0
Explanation
(a) The total energy before connection
$= \frac{1}{2} \times 4 \times 10^{- 6} \times (50)^{2} + \frac{1}{2} \times 2 \times 10^{- 6} \times (100)^{2}$
$= 1.5 \times 10^{- 2}J$
When connected in parallel
$4 \times 50 + 2 \times 100 = 6 \times V \Rightarrow V = \frac{200}{3}$
Total energy after connection
$= \frac{1}{2} \times 6 \times 10^{- 6} \times \left( \frac{200}{3} \right)^{2} = 1.33 \times 10^{- 2}\ J$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.