An alternating emf of Esint volts is supplied to a circuit containing an inductor of L henrys,

An alternating emf of Esinωt volts is supplied to a circuit containing an inductor of L henrys, a resistor of R ohms and a capacitor of C farads in series. The differential equation satisfied by the current i amps and the charge q coulombs on the capacitor is

Using i = dq/dt obtain a second-order differential equation satisfied by i. Find the resistance if it is just large enough to prevent natural oscillations. For this value of R and ω = (LC)^–1/2 prove that

where K² = L/C, when the current and charge on the capacitor are both zero at time t = 0.

Transcribed Image Text:

di dt L- + Ri + 9 C = E sin cot