A solenoid valve coil of inductance and winding resistance is connected in series…
PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Electricity, Magnetism & Electromagnetism · Electric current and circuits
Electronics for Measurement, Ch Capacitors, inductors and the time constant
Problem
A solenoid valve coil of inductance L=180mH and winding resistance R=60Ω is connected in series with an ideal switch across an ideal 24V source (the source has zero output resistance and the switch has zero resistance when closed). The switch closes at t=0; before that instant no current flows anywhere in the loop.
((a)) Starting from Kirchhoff's voltage law for the loop and the inductor law v=Ldi/dt, write the differential equation satisfied by the loop current i(t) for t≥0.
((b)) Solve this equation by separating variables, using the continuity of inductor current to fix the constant of integration, and write the result in final-value-plus-decaying-departure form.
((c)) State the time constant τ and the final current I∞ for this coil, and evaluate i(t) at t=τ and at t=3τ.