Initially k1 is closed, now if k2 is also closed. Find the h... | PHYSICS - ENERGY STORED IN A CAPACITOR | SolveeIt | Solveeit

Today, August 19

Question

Initially k₁ is closed, now if k₂ is also closed. Find the heat loss after closing of switch k₂ –

A

$\frac{1}{2}$ CV²

B

$\frac{2}{3}$ CV²

C

$\frac{1}{3}$ CV²

D

$\frac{1}{4}$ CV²

Answer

$\frac{1}{3}$ CV²

Explanation

Solution

When k₁ is closed

Q = CV

energy U_i = $\frac { 1 } { 2 }$ CV²

When k₂ is also closed

equivalent ckt

C_eq = C + =

Energy U_f = $\frac { 1 } { 2 }$ × V² = $\frac { 5 } { 6 }$ CV²

charge supplied by battery after closing k₂

= $\frac { 5 } { 3 }$ CV – CV = $\frac { 2 } { 3 }$ CV

energy supplied by battery = U_f – U_i + DH

$\frac { 2 } { 3 }$ CV² = $\frac { 5 } { 6 }$ CV² – $\frac { 1 } { 2 }$ CV² + DH

\ DH = $\frac { 1 } { 3 }$ CV²