A bench experiment uses an ideal battery (no internal resistance)

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

A bench experiment uses an ideal

15\,\mathrm{V}

battery (no internal resistance), a resistor

R_1 = 2.0\,\mathrm{k}\Omega

, a capacitor

C = 0.10\,\mu\mathrm{F}

, a coil

L = 10\,\mathrm{mH}

of negligible resistance and a resistor

R_2 = 50\,\Omega

. All switches are ideal and all connecting wires have zero resistance. The capacitor is uncharged at

t = 0

. ((a)) At

t = 0

the battery,

R_1

and

C

are connected in a single loop. Starting from Kirchhoff's loop rule with

I = dQ/dt

, derive

Q(t)

and hence

I(t)

. State the time constant and evaluate the current at

t = 0

and at

t = \tau

. ((b)) Long afterwards the battery and

R_1

are removed and the fully charged capacitor is connected to the coil alone. Write the loop rule for this loop and use it to show that

Q^2/2C + \tfrac12 LI^2

does not change with time. Hence find the largest current that flows. ((c)) At the instant the coil's current is largest, an ideal switch replaces the capacitor by

R_2

, the coil's current being continuous through the change. Derive

I(t)

for this stage from the loop rule and find how long the current takes to fall to

10

per cent of its value at that instant.

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