Question

A 90 W lightbulb is designed to operate with an applied ac voltage of 130 V rms. The bulb is placed in series with an inductor L, and this series combination is then connected to a 50 Hz 200 V voltage source.

Part A

For the bulb to operate properly, determine the required value for L. Assume the bulb has resistance R and negligible inductance.

Express your answer using two significant figures.

L=........ H

Answer 1

A)

V_rms = 130 Volts

P = power = 90 W

R = resistance

using the equation

P = V²_rms /R

90 = (130)²/R

R = 187.8 ohm

current is given as

i_rms = V_rms/R = 130/187.8 = 0.69 A

z = impedence

impedence is given as

z = V_rms/i_rms = 200/0.69 = 289.86 ohm

inductive reactance is given as

X_L = 2fL

impedence is given as

z = sqrt(R² + X_L²)

289.86 = sqrt(187.8² + X_L²)

X_L = 220.8 ohm

2fL = 220.8

2 x 3.14 x 50 L = 220.8

L = 0.7