8) An RLC circuit is used to tune a radio to an FM radio station broadcasting at

Question

8) An RLC circuit is used to tune a radio to an
FM radio station broadcasting at 34.9 MHz.
The resistance in the circuit is 6.5 ?, and capacitance is 0.8 pF.
What inductance should be present in the
circuit?
Answer in units of

When a particular inductor is connected to a sinusoidal voltage with a 149 V amplitude, a peak current of 2.6 A appears in the inductor. What is the maximum current if the frequency of the applied volt age is doubled? Answer in units of 10.0 points What is the inductive reactance at the new frequency? Answer in units of ohm A rms AC voltage of 116 V at 60 Hz is applied to an RLC circuit with 18.6 mH inductor,0.387 mu F capacitor, and 50.7 12 resistor in series.50.7ohm 18.6 mH What is the rms current? Answer in units of What Is the power factor of the circuit? What Is the power consumed in the circuit? Answer in units of W

Explanation / Answer

8

Resonant frequency

f=1/2pi*sqrt(LC)

=>L=1/4pi2f2C =1//4pi2*(34.9*106)2*(0.8*10-12)

L=26 uH

9.

Maximum current

I=V/2pifL

so

I1/I2=f2/f1

Given

f2=2f1

2.6/I2=2f1/f1

I2=1.3 A

10.

Inductive frequency

XL=V/I2 =149/1.3

XL=114.6 ohms

11

Inductive reactamce

Xl=2pifL=2pi*60*0.0186=7.012 ohms

Capacitive reactance

Xc=1/2pifC =1/2pi*60*0.387*10-6 =6854.23 ohms

Impedance

Z=sqrt[R2+(XL-Xc)2]=sqrt[50.72+(6854.23-7.012)2]

Z=6847.4 ohms

Rms current

Irms=Vrms/Z =116/6847.4

Irms=0.01694 A

12

Power factor

PF=cos(o)=R/Z =50.7/6847.4 =0.0074

13 aVERAGE POWER

Pav=VICos(o) =116*0.01694*0.0074

Pav=0.01454 watts

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