An inductor and a resistor are connected in series. When connected to a 60-Hz, 90-V (rms) source, the voltage drop across the re sistor 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.
1 answer:
Answer:
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%
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