COLLEGE PHYSICS
COLLEGE PHYSICS
2nd Edition
ISBN: 9781464196393
Author: Freedman
Publisher: MAC HIGHER
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Chapter 21, Problem 81QAP
To determine

(a)

The impedance of the circuit containing a heating coil and an ultra-capacitor connected in series to a 60.0 Hz 120 V rms supply.

Expert Solution
Check Mark

Answer to Problem 81QAP

The impedance of the circuit containing a heating coil and an ultra-capacitor connected in series to a 60.0 Hz 120 V rms supply is 2.18 O.

Explanation of Solution

Given:

Number of windings in the coil

  N=750 turns

Length of the coil

  l=8.50 cm=8.50×102m

Diameter of the coil

  d=1.25 cm=1.25×102m

Resistance of the coil

  R=2.15 Ω

Capacitance of the capacitor

  C=2240 μF=2.24×103F

Frequency of the supply

  f=60.0 Hz

The rms voltage of the supply

  Vrms=120 V

Formula used:

The heating coil behaves as an inductor. The inductance L of the coil is given by,

  L=μ0N2Al

Here, μ0 is the permeability of free space and has a value μ0=4π×107H/m, A is the area of the coil, given by,

  A=πr2=π(d2)2

And r is the radius of the coil.

Therefore, the inductance is given by,

  L=(4π× 10 7H/m)N2π( d 2 )2l=( π 2× 10 7H/m)N2d2l......(1)

The impedance of the circuit is given by,

  Z=( 1 2πfC2πfL)2+R2......(2)

Calculation:

Determine the value of inductance of the heating coil by substituting the values of variables in equation (1).

  L=( π 2× 10 7H/m)N2d2l=( 3.14)2( 10 7 H/m)( 750 turns)2( 1.25× 10 2 m)28.50×102m=1.019×103H

Substitute the value of the known variables in equation (2) and calculate the value of impedance.

  Z=( 1 2πfC 2πfL)2+R2=[ 1 2( 3.14 )( 60.0 Hz )( 2.24× 10 3 F ) 2( 3.14 )( 60.0 Hz )( 1.019× 10 3 H )]2+( 2.15 Ω)2=2.184 Ω

Conclusion:

Thus, the impedance of the circuit containing a heating coil and an ultra-capacitor connected in series to a 60.0 Hz 120 V rms supply is 2.18 O.

To determine

(b)

The rms current through of the circuit containing a heating coil and an ultra-capacitor connected in series to a 60.0 Hz 120 V rms supply.

Expert Solution
Check Mark

Answer to Problem 81QAP

The rms current through of the circuit containing a heating coil and an ultra-capacitor connected in series to a 60.0 Hz 120 V rms supply is 55 A.

Explanation of Solution

Given:

The rms voltage of the supply

  Vrms=120 V

Impedance

  Z=2.184 Ω

Formula used:

The rms current flowing in the circuit is given by,

  irms=VrmsZ

Calculation:

Calculate the rms value of the current by substituting the given values of variables in the formula.

  irms=VrmsZ=120 V2.184 Ω=54.94 A

Conclusion:

Thus the rms current through of the circuit containing a heating coil and an ultra-capacitor connected in series to a 60.0 Hz 120 V rms supply is 55 A.

To determine

(c)

The peak value of current in the circuit.

Expert Solution
Check Mark

Answer to Problem 81QAP

The peak value of current in the circuit is 77.7 A.

Explanation of Solution

Given:

The rms value of current irms=54.94 A

Formula used:

The peak value of current is given by,

  i0=2irms

Calculation:

Calculate the value of the peak current by substituting the value of irms in the formula.

  i0=2irms=2(54.94 A)=77.7 A

Conclusion:

Thus the peak value of current in the circuit is 77.7 A.

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Chapter 21 Solutions

COLLEGE PHYSICS

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