Question

A series ac circuit consists of a voltage source of frequency f = 60 Hz and source voltage amplitude 345 volts, a resistor of resistance R = 255 Ω, a capacitor of capacitance C = 6.2×10−6F, and an inductor of inductance L.

(a) What must be the value of L for the phase angle Φ to be zero?

(b) When L has the value calculated in (a), what is the current amplitude in the circuit?

Answer 1

(a) What must be the value of 'L' for the phase angle Φ to be zero?

The phase angle is given by -

= (X_L - X_C) / R

When the phase angle to be zero, then we have

X_L = X_C

L = 1 / C

L = 1 / ² C

L = 1 / (2f)² C

where, f = frequency of source = 60 Hz

C = capacitance of a capacitor = 6.2 x 10^-6 F

then, we get

L = 1 / [(4) (3.14)² (60 Hz)² (6.2 x 10^-6 F)]

L = 1.13 H

(b) When 'L' has the value calculated in Part (a), what is the current amplitude in a circuit?

Using a formula, we have

Z = R² + (X_L - X_C)²

Z = R² + (0)²

Z = R

From an Ohm's law, we get

I = V / Z = V / R

where, V = voltage amplitude = 345 V

R = resistance of a resistor = 255

then, we get

I = [(345 V) / (255 )]

I = 1.35 A