COLLEGE PHYSICS,VOLUME 1
COLLEGE PHYSICS,VOLUME 1
2nd Edition
ISBN: 9781319115104
Author: Freedman
Publisher: MAC HIGHER
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Chapter 21, Problem 80QAP
To determine

(a)

The voltage and current amplitudes for the light bulb connected to an ac generator.

Expert Solution
Check Mark

Answer to Problem 80QAP

For the bulb connected to the ac generator, the voltage amplitude is found to be 13 V and the current amplitude is 1.53 A.

Explanation of Solution

Given:

Magnetic field applied

  B=0.225 T

Number of turns

  N=33

Length of a side of the square coil

  l=15.0 cm=15.0×102m

Frequency of the generator

  f=745 rpm=74560rps

Resistance of the bulb

  R=8.50 Ω

Formula used:

The voltage amplitude is given by the expression,

  V0=NBA(2πf)

Here, A is the area of the square coil, given by,

  A=l2

Therefore,

  V0=NBl2(2πf)......(1)

The current amplitude is given by,

  i0=V0R......(2)

Calculation:

Substitute the known values of variables in equation (1) and calculate the voltage amplitude.

  V0=NBl2(2πf)=(33)(0.225 T)(15.0× 10 2m)2(2)(3.14)(74560rps)=13.03 V

Calculate the current amplitude by substituting the value of R and the calculated value of V0 in equation (2).

  i0=V0R=13.03 V8.50 Ω=1.533 A

Conclusion:

Thus, for the bulb connected to the ac generator, the voltage amplitude is found to be 13 V and the current amplitude is 1.53 A.

To determine

(b)

The average rate at which heat is generated in the bulb connected to the ac generator.

Expert Solution
Check Mark

Answer to Problem 80QAP

The average rate at which heat is generated in the bulb connected to the ac generator is 9.99 W.

Explanation of Solution

Given:

The current amplitude

  i0=1.533 A

Resistance of the bulb

  R=8.50 Ω

Formula used:

The average rate at which heat is generated in the bulb is equal to the power dissipated by the bulb. This is given by,

  Pav=irms2R

Here, irms is the rms current flowing in the bulb and it is related to the current amplitude as,

  irms=i02

Therefore,

  Pav=i022R......(3)

Calculation:

Substitute the values of the variables in equation (3) and calculate the rate at which heat is generated in the bulb.

  Pav=i022R=( 1.533 A)22(8.50 Ω)=9.988 W

Conclusion:

Thus, the average rate at which heat is generated in the bulb connected to the ac generator is 9.99 W.

To determine

(c)

The energy consumed by the bulb every hour.

Expert Solution
Check Mark

Answer to Problem 80QAP

The energy consumed by the bulb every hour is 3.6×104J.

Explanation of Solution

Given:

Average power

  Pav=9.988 W

Time interval

  Δt=1 h

Formula used:

The energy consumed by the bulb every hour is given by,

  E=PavΔt

Calculation:

Substitute the values of variables in the formula and calculate the energy consumed in one hour.

  E=PavΔt=(9.988 W)(1h×3600 s1 h)=3.595×104J=3.6×104J

Conclusion:

Thus, the energy consumed by the bulb every hour is 3.6×104J.

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Chapter 21 Solutions

COLLEGE PHYSICS,VOLUME 1

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