Question

An RLC series circuit consists of a 50 Ω resistor, a 200 μF capacitor, and a 120-mH inductor whose coil has a resistance of 20 Ω. The source for the circuit has an rms emf of 240 V at a frequency of 60 Hz. Calculate the rms voltages across the inductor.

Answer 1

182.9 Volts

Step-by-step explanation:

R = resistance of the resistor = 50 Ω

C = capacitance of the capacitor = 200 μF = 200 x 10⁻⁶ F

L = Inductance of the inductor = 120 mH = 0.12 H

f = frequency = 60 Hz

Capacitive reactance is given as

X = (2πfC)⁻¹

X = (2(3.14) (60) (200 x 10⁻⁶))⁻¹

X = 13.3 Ω

Inductive reactance is given as

X' = 2πfL

X' = 2(3.14) (60) (0.12)

X' = 45.2 Ω

Impedance of the circuit is given as

z = √(R² + (X' - X)²)

z = √(50² + (45.2 - 13.3)²)

z = 59.31 Ω

V = rms emf of the source = 240 Volts

rms voltage across the inductor is given as

V' = V z⁻¹ X'

V' = (240) (59.31)⁻¹ (45.2)

V' = 182.9 Volts