A 38.6 uF capacitor is connected to a 46.2 ohm resistor and a generator whose rm

Question

A 38.6 uF capacitor is connected to a 46.2 ohm resistor and a generator whose rms output is 23.5 V at 60.0 Hz. Calculate the rms current in the circuit.
Calculate the voltage drop across the resistor.
Calculate the voltage drop across the capacitor.

Calculate the phase angle for the circuit.
A 38.6 uF capacitor is connected to a 46.2 ohm resistor and a generator whose rms output is 23.5 V at 60.0 Hz. Calculate the rms current in the circuit.
Calculate the voltage drop across the resistor.
Calculate the voltage drop across the capacitor.

Calculate the phase angle for the circuit.

Calculate the voltage drop across the resistor. Calculate the voltage drop across the resistor.
Calculate the voltage drop across the capacitor.

Calculate the phase angle for the circuit.

Explanation / Answer

Given,

C = 38.6 uF ; R = 46.2 Ohm ; Vrms-o = 23.5 V ; f = 60 Hz

The impedence of the circuit will be:

Z = sqrt (R^2 + Xc^2)

Xc = 1/ 2 pi f C = 1/2 x 3.14 x 60 x 38.6 x 10^-6 = 68.75 Ohm

Z = sqrt (46.2^2 + 68.75^2) = 82.83 Ohm

I = V/Z = 23.5/82.83 = 0.28 A

Vr = Irms R = 0.28 x 46.2 = 12.94 Volts

Hence, Vr = 12.94 V

Vc = Irms x Xc = 0.28 x 68.75 = 19.25 V

Hence, Vc = 19.25 V

phi = cos^-1(R/Z)

phi = cos^-1(46.2/82.83) = 56.1 deg

Hence, phi = 56.1 deg

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