Two capacitors of equal capacitance $(C_{1} = C_{2})$ are as shown in figure. Initially, while the switch is open (as shown) one of the capacitors is uncharged and the other carries charge $Q_{0} .$ The energy stored in the charged capacitor is $U_{0} .$ Sometime after the switch is closed, the capacitors $C_{1}$ and $C_{2}$ carry charges $Q_{1}$ and $Q_{2}$ respectively; the energies stored in the capacitors are $U_{1}$ and $U_{2}$ respectively. Which of the following expression is correct ?

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

$Q_{0} = \frac{1}{2} (\frac{U_{1}}{Q_{1}} + \frac{U_{2}}{Q_{2}})$

$Q_{1} = Q_{2}$

$U_{0} = U_{1} + U_{2}$

$Q_{0} = \frac{1}{2} (Q_{1} + Q_{2})$

answer is A, D.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Because $C_{1} = C_{2}$ and $C_{1}, C_{2}$ are in parallel.

$∴ Q_{0} = Q_{1} = Q_{2}, ∴ Q_{0} = \frac{1}{2} (Q_{1} + Q_{2})$

Also $U_{0} = U_{1} = U_{2}, ∴ U_{0} \neq \frac{1}{2} (U_{1} + U_{2})$

$Q_{0} = \frac{1}{2} (\frac{U_{1}}{Q_{1}} + \frac{U_{2}}{Q_{2}})$ is dimensionally incorrect

Watch 3-min video & get full concept clarity