A capacitor of capacitance is initially charged to a potential difference

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

A capacitor of capacitance

C=25\,\mu\text{F}

is initially charged to a potential difference

V_0=12\,\text{V}

. At time

t=0

it is connected across a resistor of resistance

R=1.2\,\text{k}\Omega

, and the resulting current through the resistor is described by

I(t)=I_0 e^{-t/\tau}

, where

\tau=RC

. Answer the following. Show all algebraic steps, annotate your reasoning, and include correct units in your final numerical answers. (a) Express the initial current

I_0

in terms of

V_0

and

R

. (b) Derive an algebraic expression for the total charge that flows through the resistor from

t=0

t=\infty

. (c) Evaluate the numerical value of the total charge obtained in part (b). (d) Compare the value from part (c) with the initial charge stored on the capacitor before discharge. Explain any similarities or differences in physical terms.

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