New capacitance when dielectric material covers bottom half

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Homework Help Overview

The discussion revolves around a parallel plate capacitor with an initial capacitance C0, where a dielectric material with a dielectric constant K=2 is introduced, filling only the bottom half of the gap between the plates. Participants are exploring how this affects the overall capacitance.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants are discussing the calculation of the new capacitance, with one suggesting that the new capacitance can be viewed as a series combination of two capacitors, one with the dielectric and one without. Others are questioning whether the area of the plates should be adjusted and whether the distance between the plates is affected.

Discussion Status

There are multiple interpretations being explored regarding the setup of the problem and the calculations involved. Some participants have provided guidance on the relationship between the capacitors and the effects of the dielectric, while others are still seeking clarification on specific aspects of the problem.

Contextual Notes

There is a mention of the original capacitance and the need to derive the new capacitance based on the modified configuration. Participants are also considering the implications of the dielectric material on the overall capacitance without reaching a definitive conclusion.

Koh Eng Kiat
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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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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?
 
Do you need to change A to 1/2A?
 
Koh Eng Kiat said:
Do you need to change A to 1/2A?
A remains the same. Distance between the plates is halved..
 
Thanks! I solved it already!
 
Hey guys, can you tell me how exactly can I get?
 
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?
 
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