Question

A generator is connected to a resistor and a 0.049-H inductor in series. The rms voltage across the generator is 7.9 V. When the generator frequency is set to 100 Hz, the rms voltage across the inductor is 2.8 V. Determine the resistance of the resistor in this circuit

Answer 1

56.04 ohms

Step-by-step explanation:

The voltage across the inductor VL = IXL

I is the total current flowing in the circuit and XL is the inductive reactance.

First we need to get the current flowing in the circuit.

From the expression above;

I = VL/XL

Since XL = 2πfL

I = VL/ 2πfL

Given VL = 2.8V, frequancy f = 100Hz and inductance L = 0.049-H

I = 2.8/2π*100*0.049

I = 2.8/30.79

I = 0.091A

Also;

Vrms = VL + VR

VR is the voltage across the resistor.

VR = Vrms - VL

VR = 7.9 - 2.8

VR = 5.1V

Then we can calculate the resistance of the resistor

According to ohms law VR = IR

Since the inductance and resistance ar connected in series, the same current will flow through them.

R = VR/I

R = 5.1/0.091

R = 56.04 ohms

Hence the resistance of the resistor in this circuit is 56.04 ohms