Parallel plate capacitor voltage question

In summary, the voltage of a parallel-plate capacitor connected to a 100 V battery and filled with air will be 33V when the distance between the plates is increased to 3d. This is due to the inverse relationship between capacitance and distance, and the fact that voltage is directly proportional to capacitance. Therefore, the voltage increases by a factor of 3 when the distance is tripled.
  • #1
needhelpplease
14
0

Homework Statement



A parallel-plate capacitor is connected to a 100 V battery until it is fully charged. The distance between the plates is d and the space between the plates is filled with air (k=1.0). Then, the battery is disconnected. If the distance between the plates is increased to 3d, the voltage of the capacitor will be ?

Homework Equations


C=ɛ0*A/d
C=Q/V
U=QV/2
E=V/d

The Attempt at a Solution


So i know that capacitance is inversely prop. to distance. so if distance is tripled then capacitance will be 1/3 C but i cannot relate that to voltage. I know the correct answer is 33V but i cannot get my head about it. I know that if i multiply 100*1/3 i will get 33V but how does multiplying capacitance (F)by volts will give me volts.[/B]
 
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  • #2
needhelpplease said:

Homework Statement



A parallel-plate capacitor is connected to a 100 V battery until it is fully charged. The distance between the plates is d and the space between the plates is filled with air (k=1.0). Then, the battery is disconnected. If the distance between the plates is increased to 3d, the voltage of the capacitor will be ?

Homework Equations


C=ɛ0*A/d
C=Q/V
U=QV/2
E=V/d

The Attempt at a Solution


So i know that capacitance is inversely prop. to distance. so if distance is tripled then capacitance will be 1/3 C but i cannot relate that to voltage. I know the correct answer is 33V but i cannot get my head about it. I know that if i multiply 100*1/3 i will get 33V but how does multiplying capacitance (F)by volts will give me volts.[/B]
Which quantity remains the same in both the cases?
 
  • #3
cnh1995 said:
Which quantity remains the same in both the cases?
Area i believe?
 
  • #4
needhelpplease said:
Area i believe?
..and??
 
  • #5
cnh1995 said:
..and??
Area and k (dielectric)
 
  • #6
needhelpplease said:
Area and k (dielectric)
Ok. What about charge?
 
  • #7
Charge is not related?
 
  • #8
Charge has nowhere to go I believe. So wouldn't it remain consatnt?
needhelpplease said:
Charge is not related?
V=Q/C.
 
  • #9
I GOT IT. Thank you.

So as distance becomes tripled. capacitance becomes 1/3 and since capacitance is inversely proportional to voltage. so C goes 1/3 voltage is multiplied by 3 so 100*3=300V
 

1. What is a parallel plate capacitor?

A parallel plate capacitor is a type of capacitor that consists of two parallel conductive plates separated by a dielectric material. It is used to store electrical energy and is commonly found in electronic devices.

2. How does a parallel plate capacitor store charge?

When a voltage is applied to the parallel plates, an electric field is created between them. This causes electrons to accumulate on one plate, while an equal number of electrons are repelled from the other plate. This creates a potential difference between the plates, allowing the capacitor to store charge.

3. What is the formula for calculating the voltage of a parallel plate capacitor?

The formula for calculating the voltage of a parallel plate capacitor is V = Q/C, where V is the voltage, Q is the charge stored on the plates, and C is the capacitance of the capacitor. The capacitance can be calculated using the formula C = εA/d, where ε is the permittivity of the dielectric material, A is the area of the plates, and d is the distance between the plates.

4. How does the distance between the plates affect the voltage of a parallel plate capacitor?

The voltage of a parallel plate capacitor is directly proportional to the distance between the plates. This means that as the distance between the plates increases, the voltage decreases, and vice versa. This is because a larger distance results in a weaker electric field between the plates, leading to a lower potential difference.

5. What factors affect the voltage of a parallel plate capacitor?

The voltage of a parallel plate capacitor is affected by the distance between the plates, the surface area of the plates, and the dielectric material used. It is also influenced by the amount of charge stored on the plates, as well as the voltage applied to the capacitor. Additionally, the type of material used for the plates can also affect the voltage.

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