Two parallel-plate capacitors are identical except that capacitor 1 has vacuum b

Question

Two parallel-plate capacitors are identical except that capacitor 1 has vacuum between the plates and capacitor 2 has a dielectric slab of dielectric constant filling the space between the plates. Each capacitor is isolated (that is, not connected to a battery), and they store equal quantities of charge.

Part A

Compare the two capacitors based on the capacitance.

Express your answer in terms of .

Part B

Compare the two capacitors based on the potential difference between the plates.

Express your answer in terms of .

Part C

Compare the two capacitors based on the energy stored.

Express your answer in terms of .

Part D

Compare the two capacitors based on the electric field magnitude between the plates.

Express your answer in terms of .

Part E

Compare the two capacitors based on the energy density.

Express your answer in terms of .

Explanation / Answer

Here ,

1) as the capacitance is given as

Capacitance = epsilon_0 * area ( k/seperation)

for C1/C2 = 1/k

part B)

as the charge is equal

C1 * V1 = C2 * V2

V1/V2 = C2/C1

V1/V2 = k

part c)

as the energy stored = 0.5 * Q^2/C

for same charge

U1/U2 = C2/C1

U1/U2 = k

part D)

as the eletic field is V/d

E1/E2 = V1/V2

E1/E2 =k

part E)

as the volume is same for both capacitors

energy density of 1 /energy denstity of 2 = U1/U2

energy density of 1 /energy denstity of 2 = k

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