A 11.5 μF capacitor is connected to a power supply that keeps a constant potential difference of 26.0 V across the plates. A piece of material having a dielectric constant of 3.75 is placed between the plates, completely filling the space between them.

a. How much energy is stored in the capacitor before the dielectric is inserted?
b. How much energy is stored in the capacitor after the dielectric is inserted?
c. By how much did the energy change during the insertion?

a)    

b)

c)

Explanation:

A capacitor is an electronic instrument widely used in circuits and electronic tools. It is usually a pair of parallel plates used to store charge. The energy stored in the capacitor (E) is related with the charge (Q) on the plates and the potential difference across the plates as:

(1)

Capacitance is the charge over the potential difference (with Faraday (F) units):

(2)

Using (2) on (1):

(2)

That is the energy stored on a capacitor in terms of the potential difference and the capacitance

a)

The dielectric constant (k) of a material is the defined as the capacitance the capacitor increases due the dielectric (C) over the initial capacitance (Co):

So, the new capacitance is

Using this value on (2)

b)

c) Subtracting the result obtained on a) of b) the energy change during the insertion of the dielectric is

the electric field is a “force field” around a charged object that illustrates the direction the electric force would push an imaginary