An inductor and a resistor are connected in series. When connected to a 60-Hz, 90-V (rms) source, the voltage drop across the resistor is found to be 51 V (rms) and the power delivered to the circuit is 17 W. (a) Find the value of the resistance.

(b) Find the value of the inductance.

resistance = 154.54 ohm

inductance is 59.60%

Explanation:

given data

frequency f = 60 Hz

V rms = 90 V

V rms = 51 V

power P = 17 W

to find out

resistance and inductance

solution

we will apply here power formula here to find current I

power = I (Vrms)

I = 17 / 51 = 0.33

current I = 0.33 A

so resistance formula is

resistance = V / I

resistance = 51 / 0.33

resistance = 154.54 ohm

and

we know inductance L formula

x = 2πfL

so L = x / 2πf ... a

we know

x = √ (Z² - R²)

x = √ ((90/0.33) ² - (154.54²))

x = 224.71

so from equation a

L = 224.71 / 2π (60)

L = 0.5960

so inductance is 59.60%