A capacitor of capacitance discharges through a resistor of resistance

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Electricity, Magnetism & Electromagnetism · Electric current and circuits

Mathematical Methods for Physics, Ch First-order differential equations and physical modelling

Problem

A capacitor of capacitance

C=100\,\mu\mathrm{F}

discharges through a resistor of resistance

R=25\,\mathrm{k\Omega}

, starting from

V(0)=10.0\,\mathrm{V}

. Its voltage obeys

\dot{V}=-V/\tau

with

\tau=RC

. (a) Using the direction field of

\dot{V}=-V/\tau

, state the equilibrium voltage and, from the sign of

\partial\dot{V}/\partial V

there, say whether it is stable. (b) Find the time for

V

to fall to half its initial value. (c) Find the time for

V

to fall to

5\%

of its initial value.

Related theory

Ordinary differential equations

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