# capacitance problem

#### logearav

Joined Aug 19, 2011
243
A dielectric of dielectric constant 3 fills three fourth of the space between plates of a parallel plate capacitor. What percentage of the energy is stored n the dielectric?
My attempt to solve this is given in attachment.

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#### t_n_k

Joined Mar 6, 2009
5,455
C1 is the free space capacitance
C2 is the filled space capacitance

C1 & C2 are effectively in series

$$C_1=\frac{\epsilon_0 A}{d/4}=\frac{4\epsilon_0 A}{d}$$

$$C_2=\frac{3\epsilon_0 A}{3d/4}=\frac{4\epsilon_0 A}{d}$$

Where A is the plate area and d is the total plate separation distance.

So C1=C2

Being equal and in series they will each have half of the total voltage applied to the capacitance.

Having equal voltage & equal capacitance means they have equal energy - so they share half the total energy stored on their combined equivalent series capacitance.

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