Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12

# A Capacitor of Capacitance C is Given a Charge Q. At T = 0, It is Connected to an Ideal Battery of Emf ε Through a Resistance R. Find the Charge on the Capacitor at Time T. - Physics

Sum

A capacitor of capacitance C is given a charge Q. At t = 0, it is connected to an ideal battery of emf ε through a resistance R. Find the charge on the capacitor at time t.

#### Solution

Given:-

Initial charge given to the capacitor = Q

When the capacitor is connected to a battery, it will charge through the battery. The initial charge will also decay.

The growth of charge across the capacitor due to the battery of emf E,

$q = CE\left( 1 - e^{- \frac{t}{RC}} \right)$

The decay of charge through the capacitor,

$q' = Q e^{- \frac{t}{RC}}$

The net charge on the capacitor at any time t,

$q_{net} = q + q'$

$= CE\left( 1 - e^{- \frac{t}{RC}} \right) + Q e^{- \frac{t}{RC}}$

Concept: Energy Stored in a Capacitor
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#### APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 10 Electric Current in Conductors
Q 84 | Page 203