New capacitance when dielectric material covers bottom half

[Koh Eng Kiat]

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.

 

[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?

 

[Koh Eng Kiat]

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

 

[cnh1995]

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

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

 

[Koh Eng Kiat]

Thanks! I solved it already!

 

[Amr Ayman]

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

 

[cnh1995]

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

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

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?