A circuit driven by an AC generator consists of an 8-ohm resistor in series with
ID: 1493673 • Letter: A
Question
A circuit driven by an AC generator consists of an 8-ohm resistor in series with a 0.7-henry inductor, followed by a 0.1-farad capacitor. The current through the circuit is given by I=0.1cos(10t+30°) A. Find the equation for the voltage of the generator as a function of time.Special problem: What was the power factor in the previous problem? A circuit driven by an AC generator consists of an 8-ohm resistor in series with a 0.7-henry inductor, followed by a 0.1-farad capacitor. The current through the circuit is given by I=0.1cos(10t+30°) A. Find the equation for the voltage of the generator as a function of time.
Special problem: What was the power factor in the previous problem?
Explanation / Answer
let,
resistor, R=8ohm
inductor, L=0.7 ohm
capacitor, C=0.1 F
current, i=0.1*cos(10*t+30) A
=====> angular frequency, w=10 rad/sec
angular frequency, w=2pi*f
10=2pi*f
===> frequency f=16 Hz
now,
impedance Z=sqrt(R^2+(XL-XC)^2)
Z=sqrt(8^2+(w*L-1/(w*C))
Z=sqrt(8^2+(10*0.7-1/(10*0.1))
Z=8.37 ohms
a)
voltage relation , v=i*Z
V=0.1*cos(10*t+30)*8.37
v=0.837*cos((10*t+30))----? volts
b)
power factor=R/Z
=8.8/(8.37)
=1.05
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