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Chapter 4: Q41E (page 811)

When a 360-nF air capacitor (1 nF = 10-9 F) is connected to a power supply, the energy stored in the capacitor is 1.85脳10-5J. While the capacitor is kept connected to the power supply, a slab of dielectric is inserted that completely fills the space between the plates. This increases the stored energy by 2.32脳10-5J. (a) What is the potential difference between the capacitor plates? (b) What is the dielectric constant of the slab?

Short Answer

Expert verified
  1. The potential difference between the capacitor plates is 10.1 V
  2. The dielectric constant of the slab is 2.25.

Step by step solution

01

(a) Determination of the potential difference between the capacitor plates.

The capacitor is maintained under the constant potential difference because the plates are connected to the battery.

U=12C0V2

Here, U is the energy stored, C0 is the capacitance and V is the voltage.

V=2U0C0=21.85脳10-5J360脳10-9F=10.1V

Thus, the potential difference between the plates is 10.1 V.

02

(b) Determination of the dielectric constant of the slab.

The dielectric constant is expressed as,

K=CC0

As the potential difference V is constant, then,

CC0=UU0

So, Rearrange and write the equation for K,

K=UU0=1.85脳10-5J+2.32脳10-5J1.85脳10-5J=2.25

Thus, the dielectric constant is 2.25.

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