A pulsed magnet rig charges a capacitor through a resistor from an ideal supply (no…

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 pulsed magnet rig charges a

470\,\mu\mathrm{F}

capacitor through a

1.0\,\mathrm{k}\Omega

resistor from an ideal

200\,\mathrm{V}

supply (no internal resistance), then fires it into a coil of self-inductance

1.2\,\mathrm{mH}

whose resistance is negligible. All switches are ideal and all wires have zero resistance; the capacitor starts uncharged. ((a)) From Kirchhoff's loop rule derive

Q(t)

and

I(t)

for the charging stage. By integrating the current over all time find the total charge the supply pushes round the circuit, and hence the energy the supply delivers; then by integrating

I^2R

show that the resistor turns exactly half of it into heat, whatever the value of

R

. Give the three energies in joules. ((b)) Once the capacitor is fully charged the supply and resistor are disconnected and the capacitor is fired into the coil. Using the loop rule for that loop, show that

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

is constant, and find the peak current in the coil. ((c)) At the instant of peak current a switch puts an

8.0\,\Omega

resistor across the coil in place of the capacitor, the coil's current being continuous. Derive

I(t)

and find the total charge that passes through that resistor before the current dies away.

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