An initially uncharged capacitor of capacitance is charged through a resistor from an…

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electric current and circuits · Electromagnetic induction and alternating-current circuits

Electricity, Magnetism and Electromagnetism, Ch Transients: RC, RL and LC circuits

Problem

An initially uncharged capacitor of capacitance

C = 4.7\,\mu\mathrm{F}

is charged through a resistor

R = 220\,\mathrm{k}\Omega

from an ideal

9.0\,\mathrm{V}

battery of negligible internal resistance. The connecting wires have no resistance. ((a)) How long after the switch is closed does the charge on the capacitor reach

90\%

of its final value? ((b)) The same capacitor, once charged, is disconnected from the battery and connected across a coil of self-inductance

L = 2.0\,\mathrm{mH}

whose resistance is negligible, so that the circuit oscillates freely. Find the natural angular frequency

\omega_0

and the frequency

f

of the oscillation.

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