An ignition coil of self-inductance has winding resistance and is connected through a…
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 ignition coil of self-inductance L=8.0mH has winding resistance r=4.0Ω and is connected through a switch to an ideal 12V battery (no internal resistance). A capacitor C=0.22μF, initially uncharged, is wired so that when the switch opens the coil's current is forced into it. All wires have zero resistance.
((a)) The switch is closed at t=0 with no current in the coil. From Kirchhoff's loop rule derive I(t), state the time constant and the final current, and evaluate I at t=1.0ms.
((b)) Long afterwards the switch is opened, and the coil's current (which cannot jump) flows into the capacitor. For this fast stage the coil's resistance may be neglected, because the transient lasts tens of microseconds while L/r is milliseconds. Show from the loop rule for the coil and capacitor that 21LI2+Q2/2C stays constant, and hence find the peak voltage reached across the capacitor.
((c)) After the transient the capacitor, holding that peak voltage, is left connected to a 100kΩ safety resistor. Derive its charge as a function of time from the loop rule, and find how long the capacitor voltage takes to fall to 1.0V.