COLLEGE PHYSICS
COLLEGE PHYSICS
2nd Edition
ISBN: 9781464196393
Author: Freedman
Publisher: MAC HIGHER
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Chapter 17, Problem 87QAP
To determine

(a)

Capacitance of the parallel plate capacitor

Expert Solution
Check Mark

Answer to Problem 87QAP

Capacitance of the parallel plate capacitor is εoA2d(3k2k3k2+k3+k12).

Explanation of Solution

Given:

The given capacitance diagram

  COLLEGE PHYSICS, Chapter 17, Problem 87QAP , additional homework tip  1

Figure.1

Formula used:

The capacitance of the parallel plate capacitor is given as
C=kεoAd

Here,
k is the dielectric constant
εo is the permeability
A is the area
d is the distance between plates

Calculation:

It is clear from the figure.1 that capacitor with dielectric constant k2andk3 are in series connection, and the combination of these is in parallel connection with capacitor of dielectric constant of k1

Therefor the equivalent capacitance of the arrangement is calculated as
Ceq=(1 1 k 2 ε o ×3A 4× d 2 + 1 k 3 ε o ×3A 4× d 2 )+k1εoA4d=εoA2d( 3 k 2 k 3 k 2 + k 3 + k 1 2)

Conclusion:

Capacitance of the parallel plate capacitor is εoA2d(3k2k3k2+k3+k12).

To determine

(b)

Capacitance of the parallel plate capacitor

Expert Solution
Check Mark

Answer to Problem 87QAP

Capacitance of the parallel plate capacitor is εoA2d(3k2k2+1+k12).

Explanation of Solution

Given:

The given capacitance diagram

  COLLEGE PHYSICS, Chapter 17, Problem 87QAP , additional homework tip  2

Figure.1

Formula used:

The capacitance of the parallel plate capacitor is given as
C=kεoAd

Here,
k is the dielectric constant
εo is the permeability
A is the area
d is the distance between plates

Calculation:

It is clear from the figure.1 that capacitor with dielectric constant k2andk3 are in series connection, and the combination of these is in parallel connection with capacitor of dielectric constant of k1

If the dielectric with constant k3 is replace by air, k=1 than the equivalent capacitance of the arrangement is calculated as
Ceq=(1 1 k 2 ε o ×3A 4× d 2 + 1 1× ε o ×3A 4× d 2 )+k1εoA4d=εoA2d( 3 k 2 k 2 +1+ k 1 2)

Conclusion:

Capacitance of the parallel plate capacitor is εoA2d(3k2k2+1+k12).

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Chapter 17 Solutions

COLLEGE PHYSICS

Ch. 17 - Prob. 11QAPCh. 17 - Prob. 12QAPCh. 17 - Prob. 13QAPCh. 17 - Prob. 14QAPCh. 17 - Prob. 15QAPCh. 17 - Prob. 16QAPCh. 17 - Prob. 17QAPCh. 17 - Prob. 18QAPCh. 17 - Prob. 19QAPCh. 17 - Prob. 20QAPCh. 17 - Prob. 21QAPCh. 17 - Prob. 22QAPCh. 17 - Prob. 23QAPCh. 17 - Prob. 24QAPCh. 17 - Prob. 25QAPCh. 17 - Prob. 26QAPCh. 17 - Prob. 27QAPCh. 17 - Prob. 28QAPCh. 17 - Prob. 29QAPCh. 17 - Prob. 30QAPCh. 17 - Prob. 31QAPCh. 17 - Prob. 32QAPCh. 17 - Prob. 33QAPCh. 17 - Prob. 34QAPCh. 17 - Prob. 35QAPCh. 17 - Prob. 36QAPCh. 17 - Prob. 37QAPCh. 17 - Prob. 38QAPCh. 17 - Prob. 39QAPCh. 17 - Prob. 40QAPCh. 17 - Prob. 41QAPCh. 17 - Prob. 42QAPCh. 17 - Prob. 43QAPCh. 17 - Prob. 44QAPCh. 17 - Prob. 45QAPCh. 17 - Prob. 46QAPCh. 17 - Prob. 47QAPCh. 17 - Prob. 48QAPCh. 17 - Prob. 49QAPCh. 17 - Prob. 50QAPCh. 17 - Prob. 51QAPCh. 17 - Prob. 52QAPCh. 17 - Prob. 53QAPCh. 17 - Prob. 54QAPCh. 17 - Prob. 55QAPCh. 17 - Prob. 56QAPCh. 17 - Prob. 57QAPCh. 17 - Prob. 58QAPCh. 17 - Prob. 59QAPCh. 17 - Prob. 60QAPCh. 17 - Prob. 61QAPCh. 17 - Prob. 62QAPCh. 17 - Prob. 63QAPCh. 17 - Prob. 64QAPCh. 17 - Prob. 65QAPCh. 17 - Prob. 66QAPCh. 17 - Prob. 67QAPCh. 17 - Prob. 68QAPCh. 17 - Prob. 69QAPCh. 17 - Prob. 70QAPCh. 17 - Prob. 71QAPCh. 17 - Prob. 72QAPCh. 17 - Prob. 73QAPCh. 17 - Prob. 74QAPCh. 17 - Prob. 75QAPCh. 17 - Prob. 76QAPCh. 17 - Prob. 77QAPCh. 17 - Prob. 78QAPCh. 17 - Prob. 79QAPCh. 17 - Prob. 80QAPCh. 17 - Prob. 81QAPCh. 17 - Prob. 82QAPCh. 17 - Prob. 83QAPCh. 17 - Prob. 84QAPCh. 17 - Prob. 85QAPCh. 17 - Prob. 86QAPCh. 17 - Prob. 87QAPCh. 17 - Prob. 88QAPCh. 17 - Prob. 89QAPCh. 17 - Prob. 90QAPCh. 17 - Prob. 91QAPCh. 17 - Prob. 92QAPCh. 17 - Prob. 93QAPCh. 17 - Prob. 94QAPCh. 17 - Prob. 95QAPCh. 17 - Prob. 96QAPCh. 17 - Prob. 97QAPCh. 17 - Prob. 98QAPCh. 17 - Prob. 99QAPCh. 17 - Prob. 100QAPCh. 17 - Prob. 101QAPCh. 17 - Prob. 102QAPCh. 17 - Prob. 103QAPCh. 17 - Prob. 104QAPCh. 17 - Prob. 105QAPCh. 17 - Prob. 106QAPCh. 17 - Prob. 107QAPCh. 17 - Prob. 108QAP
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