# New capacitance when dielectric material covers bottom half

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1. Mar 28, 2016

### Koh Eng Kiat

1. The problem statement, all variables and given/known data

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?
2. Relevant equations

C = Q/V = κɛ0A/d

3. 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.

2. Mar 28, 2016

### cnh1995

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. Mar 28, 2016

### Koh Eng Kiat

Do you need to change A to 1/2A?

4. Mar 28, 2016

### cnh1995

A remains the same. Distance between the plates is halved..

5. Mar 28, 2016

6. Apr 1, 2016

### Amr Ayman

Hey guys, can you tell me how exactly can I get?

7. Apr 2, 2016