New capacitance when dielectric material covers bottom half

In summary, to calculate the new capacitance after inserting a dielectric material with K=2 into a parallel plate capacitor with capacitance C0, you can use the formula Cf = 3/2 Co. This is because the new capacitance is a series combination of two capacitors, one with k=2 and the other with k=1 (upper half). The distance between the plates remains the same, but the area is halved.
  • #1
Koh Eng Kiat
10
0

Homework Statement



The plates of a parallel plate capacitor of capacitance C0 are
horizontal. Into the gap a slab of dielectric material with K=2 is placed,
filling the bottom half of the gap between the plates. What is the
resulting new capacitance?

Homework Equations



C = Q/V = κɛ0A/d

The Attempt at a Solution



Co = ɛ0A/d
Cf = kɛ0A/d = ((ɛ0)(0.5A)/d) + ((2ɛ0)(1/2a)/(d)) = (ɛ0A/2d) +(ɛ0A/d) = (ɛ0A/d) + (2ɛ0A/2d) = (3ɛ0A/2d)
Cf = 3/2 Co

The correct answer is 4/3 Co. Guys, can anyone help me out? I have no idea how to derive the correct answer.
 
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  • #2
The new capacitance is a series combination of two capacitors, one with k=2 and the other with k=1(upper half). If the original capacitance was C, what values do you get for these new series capacitances?
 
  • #3
Do you need to change A to 1/2A?
 
  • #4
Koh Eng Kiat said:
Do you need to change A to 1/2A?
A remains the same. Distance between the plates is halved..
 
  • #5
Thanks! I solved it already!
 
  • #6
Hey guys, can you tell me how exactly can I get?
 
  • #7
Amr Ayman said:
Hey guys, can you tell me how exactly can I get?
cnh1995 said:
A remains the same. Distance between the plates is halved..
cnh1995 said:
The new capacitance is a series combination of two capacitors, one with k=2 and the other with k=1(upper half). If the original capacitance was C, what values do you get for these new series capacitances?
 
  • Like
Likes Amr Ayman

FAQ: New capacitance when dielectric material covers bottom half

1. What is capacitance?

Capacitance is the ability of a material to store an electrical charge when a voltage is applied.

2. How does the dielectric material affect capacitance?

The dielectric material, which is an insulating material, increases capacitance by reducing the electric field and allowing more charge to be stored.

3. What is meant by "covering the bottom half"?

In this context, "covering the bottom half" refers to placing a dielectric material between the two conductive plates of a capacitor, with the material covering the bottom half of the plates.

4. Does the type of dielectric material used affect capacitance?

Yes, the type of dielectric material used can affect capacitance as different materials have different dielectric constants, which determine the extent to which they can store charge.

5. How does the new capacitance compare to the original capacitance without the dielectric material?

The new capacitance will be higher than the original capacitance without the dielectric material, as the addition of the dielectric material increases the capacitance of the system.

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