   Chapter 16, Problem 6CQ

Chapter
Section
Textbook Problem

An air-filled parallel-plate capacitor with capacitance C0 stores charge Q on plates separated by distance d. The potential difference across the plates is ΔV0 and the energy stored is PEC,0. If the capacitor is disconnected from its voltage source and the space between the plates is then filled with a dielectric of constant κ = 2.00, evaluate the ratios (a) Cnew/C0, (b) ΔVnew/ΔV0, and (c) PEC,new/PEC,0.

(a)

To determine

The ratio CnewC0.

Explanation

Formula to calculate the capacitance is,

C=κε0A0d

• ε0 is the permittivity of free space.
• A0 is the area.
• d is the distance of separation.
• κ is the dielectric constant.

The capacitance is directly proportional to the dielectric constant. Therefore, when the dielectric constant is doubled, capacitance gets doubled

(b)

To determine

The ratio ΔVnewΔV0.

(c)

To determine

The ratio PEnewPE0.

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