A series ac circuit is shown. The inductor has a reactance of 86 Ohm and an indu

Question

A series ac circuit is shown. The inductor has a reactance of 86 Ohm and an inductance of 132 mH. A 105 Ohm resistor and a capacitor, whose reactance is 166 Ohm, are also in the circuit. The rms current in the circuit is 2 A. In Figure, the phase angle (in degrees) of the circuit is: Consider a series LRC circuit with R=54 Ohm, L=0.24 H and C=0.8 mu F. The current is 5 mA amplitude at 1.3 kHz. Remember w = 2-nf, where f is the frequency in cycles per second or Hz. Find the angular resonant frequency of oscillations. Express the answer with one decimal place.

Explanation / Answer

1.

Given

Inductive reactance

XL=86 ohms

Capacitive reactance

Xc=166 ohms

Resistance

R=105 ohms

Phase angle

o=tan^-1(XL-Xc/R)

o=tan^-1(86-166/105)

o=-37.3 degrees

2.

Resonant frequency

f=1/2pi*sqrt(LC)

f=1/2pi*sqrt(0.24*0.8*10^-6)

f=363.22 Hz

angular resonant frequency

W=2pif =2pi*363.22

W=2282.2 rad/s

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