An AC source operating at 60 Hz with a maximum voltage of 174 V is connected in

Question

An AC source operating at 60 Hz with a maximum voltage of 174 V is connected in series with a resistor (R = 1.6 k Ohm) and a capacitor (C = 2.5 mu F). (a) What is the maximum value of the current in the circuit? (b) What are the maximum values of the potential difference across the resistor and the capacitor? Delta V_R, max = V Delta V_L, max = V (c) When the current is zero, what are the magnitudes of the potential difference across the resistor, the capacitor, and the AC source? Delta V_R = V Delta V_C = V Delta V_source = V How much charge is on the capacitor at this instant? Delta q_c = mu C (d) When the current is at a maximum, what are the magnitudes of the potential differences across the resistor, the capacitor, and the AC source? Delta V_R = V Delta V_C = V Delta V_source = V How much charge is on the capacitor at this instant? Delta q_c = mu C

Explanation / Answer

(A) R = 1600 ohm

Xc = 1 / (2 pi f C) = 1 / (2 x pi x 60 x 2.5 x 10^-6)

Xc = 1061 ohm

Z = sqrt[ R^2 + Xc^2] = 1919.8 ohm

Imax = Vmax / Z = 0.0906 A

(b) VR = I R = 145 Volt

VC = I Xc = 96.2 Volt

(c) when current is the that means Vsource = VR = Vc = 0

Qc = 0

(D) Vsource = 174 V

VR= 145 Volt

VC = 96.2 Volt

Q = C Vc = 2.5 x 10^-6 x 96.2 = 240.4 uC

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