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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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