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 dissipated in the resistances of connecting wires

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 circuit

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