Question

Consider an RC circuit with R = 1.60 k? , C = 1.50 ?F . The rms applied voltage is 240 V at 60.0 Hz.

What is the rms current in the circuit?

What is the phase angle between voltage and current?

What are the voltmeter readings across R and C?

Answer 1

R = resistance = 1600 ohm

C = Capacitance = 1.50 x 10^-6 F

f = frequency = 60 Hz

X_c = Capacitive reactance = 1/(2fC) = 1/(2 x 3.14 x 60 x 1.50 x 10^-6) = 1769.3 ohm

impedence is given as

z = sqrt(R² + X_c²) = sqrt((1600)² + (1769.3)²) = 2385.5 ohm

rms current is given as

i_rms = V_rms/z = 240/2385.5 = 0.101 A

phase angle is given as

= tan^-1(X_c/R) = tan^-1(1769.3/1600) = 48 deg

V_r = Voltage across resistor = i_rms R = (0.101) (1600) = 161.6 Volts

V_c = V_rms - V_r = 240 - 161.6 = 78.4 Volts