A series ac circuit is shown. The inductor has a reactance of 80 ohms and an ind

Question

A series ac circuit is shown. The inductor has a reactance of 80 ohms and an inductance of 150 mH. A 50 ohm resistor and a capacitor whose reactance is 100 ohms are also in the circuit. The rms current in the circuit is 2.4 A. In the figure, the voltage amplitude across the capacitor is closest to:

A series ac circuit is shown. The inductor has a reactance of 80 ohms and an inductance of 150 mH. A 50 ohm resistor and a capacitor whose reactance is 100 ohms are also in the circuit. The rms current in the circuit is 2.4 A. In the figure, the voltage amplitude across the capacitor is closest to:

Explanation / Answer

First we need the angular frequency omega. Omega = 2*pi*f = 2*50*pi = 314 rad/s
a) Inductive reluctance (XL)= omega *L =314*.150 = 47.1 ohms


Impedance (Z) = sqrt (R^2 + (omega*L - 1/omega*C)^2) = sqrt(140^2 +(78.5 - 1592)^2) = 1520 ohms

d) I max = v/Z = 210/1520 = 0.138A

e) Phase angle Phi = arctan ((XL - XC)/R ) = arctan ((78.5-1592)/140) = -84.7deg

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