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A parallel-plate capacitor is connected to a battery. After it becomes charged, the capacitor is disconnected from the battery and the plate separation is increased.

What happens to the potential difference between the plates?

A) More information is needed to answer this question
B) The potential difference between the plates stays the same.
C) The potential difference between the plates decreases.
D) The potential difference between the plates increases.

User Bmaupin
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1 Answer

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Answer:

D) The potential difference between the plates increases.

Step-by-step explanation:

The capacitance of a parallel plate capacitor having plate area A and plate separation d is C=ϵ0A/d.

Where ϵ0 is the permittivity of free space.

A capacitor with increased distance, will have a new capacitance C1=ϵ0kA/d1

Where d1 = nd

since d1 > d

therefore n >1

n is a factor derived as a result of the increased distance

Therefore the new capacitance becomes:

C1=ϵ0A/d1

C1= ϵ0A/nd

C1= C/n -------1

Where C1 is the capacitance with increased distance.

This implies that the charge storing capacity of the capacitor with increased plate separation decreases by a factor of (1/n) compared to that of the capacitor with original distance.

Given points

The charge stored in the original capacitor Q=CV

The charge stored in the original capacitor after inserting dielectric Q1=C1V1

The law of conservation of energy states that the energy stored is constant:

i.e Charge stored in the original capacitor is same as charge stored after the dielectric is inserted.

Charge before plate separation increase same as after plate separation increase

Q = Q1

CV = C1V1

 CV = C1V1 -------2

We derived C1=C/n in equation 1. Inserting this into equation 2

CV = (CV1)/n

V1 = n(CV)/C

= n V

Since n > 1 as a result of the derived new distance, the new voltage will increase

User Mat J
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