An 75.0 resistor and a 200 mH inductor are connected in parallel across a 105 V (rms), 60.0 Hz source.
(a) What is the rms current in the resistor? Find in Amps
(b) By what angle does the total current lead or lag behind the
voltage?
The current lags the voltage by (find degrees)
here,
R = 75 ohm
L = 200 mH
L = 0.2 H
voltage , V = 105 V
frequency , f = 60 Hz
A)
Current in resistor = (105 V) / (75 Ohms) = 1.4 Amps (RMS)
B)
Inductive reactance: 2 Pi f L = 2 Pi (60 Hz)(0.2 H) = 75.4 Ohms
Impedance of parallel combination
Z = (75.4 i)(75) / ( 75.4i + 50 )
Z = 136.41 - 88.77i = 162.75 Ohms at 62.57 degrees
The total current is therefore (105 V) / Z = 0.64 Amps and cureent lead the volatge by 62.57 degrees
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