COLLEGE PHYSICS LL W/ 6 MONTH ACCESS
COLLEGE PHYSICS LL W/ 6 MONTH ACCESS
2nd Edition
ISBN: 9781319414597
Author: Freedman
Publisher: MAC HIGHER
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Chapter 21, Problem 82QAP
To determine

The value of the rms current if the frequency of the supply is changed to 60.0 Hz.

Expert Solution & Answer
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Answer to Problem 82QAP

If the frequency of the supply is changed to 60.0 Hz, the rms current flowing in the circuit is 57.3 mA.

Explanation of Solution

Given info:

Capacitance of the capacitor

  C=15.0 μF=15.0×106F

Voltage amplitude

  V0=25.0 V

Resonant frequency

  f0=44.5 Hz

Maximum rms current

  (irms)max=65.0 mA=65.0×103A

New frequency

  f=60.0 Hz

Formula used:

When the current flowing in a RLC circuit connected to an ac supply is maximum, the frequency of the source is equal to Resonant frequency. When the circuit is in resonance, the impedance of the circuit is purely resistive. Therefore, the resistance R of the RLC circuit is given by,

  R=Vrms( i rms)max

Where, the rms voltage is given by,

  Vrms=V02

Therefore,

  R=V02( i rms)max......(1)

The resonant frequency is related to the inductance L and the capacitance C as follows:

  f0=12π1LC

Rewrite the equation for L.

  L=14π2f02C......(2)

Using the values of L and R calculated using equations (1) and (2) the impedance Z of the circuit at a frequency f can be calculated using the expression:

  Z=( 1 2πfC2πfL)2+R2......(3)

The rms current flowing in the circuit at a frequency f is given by,

  irms=VrmsZ=V02Z......(4)

Calculation:

Calculate the resistance R of the circuit by substituting the known values of the variables in equation (1).

  R=V02( i rms )max=25.0 V2(65.0× 10 3A)=2.716×102Ω

Calculate the inductance of the circuit by substituting the known values of the variables in equation (2).

  L=14π2f02C=14( 3.14)2( 44.5 Hz)2(15.0× 10 6F)=0.8536 H

Calculate the value of impedance of the circuit at a frequency 60.0 Hz by substituting the known values of the variables in equation (3).

  Z=( 1 2πfC 2πfL)2+R2=[ 1 2( 3.14 )( 60.0 Hz )( 15.0× 10 6 F ) 2( 3.14 )( 60.0 Hz )( 0.8536 H )]2+( 2.716× 10 2 Ω)2=3.083×102 Ω

Finally determine the rms value of current flowing in the circuit at the frequency 60.0 Hz by substituting the values of the variables in equation (4).

  irms=VrmsZ=V02Z=25.0 V2(3.083× 10 2 Ω)=5.732×102A=57.3 mA

Conclusion:

Thus, if the frequency of the supply is changed to 60.0 Hz, the rms current flowing in the circuit is 57.3 mA.

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Chapter 21 Solutions

COLLEGE PHYSICS LL W/ 6 MONTH ACCESS

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