Question

A capacitor of unknown capacitance, a coil of inductance L, and a resistor of resistance R are connected to a source of a.c. voltage ξ = ξ₀ cos ωt (Fig. 112). 

The current in the circuit is I = (ξ₀/R) cos ωt

Determine the amplitude U₀ of the voltage across the capacitor plates.

Answer 1

Since the current and the voltage vary in phase, and the amplitude of current is I = ξ₀/R (i.e. the contributions from C and L are compensated) we have

From the relations U_c = q/C and dq/dt = I, we obtain

Therefore, the amplitude of the voltage across the capacitor plates is