Conceptual Physics

26.9 - Sample problem: dielectric and potential difference

Variables

Strategy

1. Use the definition of capacitance, and the equation for capacitance with a dielectric present, to determine the potential difference when
   the dielectric is present.

Physics principles and equations

The definition of capacitance is

C = q/ǻV

The relation between capacitances with and without a dielectric present is

Cț = țC

Charge in any isolated system is conserved.

Step-by-step solution

We use the definition of capacitance twice; once when the dielectric is not present, and again when it is. The amount of charge remains

constant since the capacitor is isolated.

Now we combine the above expressions to find a relation between the potential differences with and without a dielectric present. We evaluate

the resulting equation to answer the problem.

The potential difference between the plates after inserting the dielectric turns out to be the original potential difference divided by the dielectric

constant. The higher the dielectric constant, the more the potential difference will be decreased after the dielectric is introduced.

A battery causes the plates of a

capacitor to charge so that the

potential difference between them is

9.0 V. The capacitor is then isolated

so that its charge remains constant

and the battery no longer acts on it.

After a dielectric (Ȁ = 16) is inserted

between the plates, what is the

potential difference between them?

initial potential difference ǻV = 9.0 V

initial capacitance C

charge on capacitor q

dielectric constant of material ț = 16

capacitance with dielectric present Cț

potential difference with dielectric present ǻVț

Step Reason

1. q = CǻV definition of capacitance

2. Cț = țC capacitance with dielectric

3. definition of capacitance

Step Reason

4. substitute equations 1 and 2 into equation 3

5. simplify

6. evaluate

(^484) Copyright 2000-2007 Kinetic Books Co. Chapter 26