Charging a Condenser with a Dielectric Medium

Introduction:
When a condenser (also known as a capacitor) is charged, it stores electrical energy in the form of an electric field between its plates. The energy stored in a condenser can be calculated using the formula E = 1/2 * C * V^2, where E is the energy, C is the capacitance, and V is the potential difference (p.d.) across the condenser.

In this scenario, the condenser is charged to a p.d. of 120 volts and has an initial energy of 1/100000 J. We are then introducing a dielectric medium with a relative permittivity (εr) of E-5 between the plates. Let's explore how the introduction of the dielectric medium affects the energy stored in the condenser.

Effect of Dielectric Medium:
When a dielectric medium is inserted between the plates of a condenser, it increases the capacitance of the condenser. The capacitance of a condenser with a dielectric medium can be calculated using the formula C' = εr * C, where C' is the new capacitance and εr is the relative permittivity.

Calculation:
Given that the initial energy (E) is 1/100000 J and the p.d. (V) is 120 volts, we can rearrange the energy formula to solve for the initial capacitance (C).

E = 1/2 * C * V^2
1/100000 = 1/2 * C * (120)^2
C = (1/100000) / (1/2 * (120)^2)
C = 1/100000 / 1/28800
C = 28800/100000
C = 0.288 F

The initial capacitance of the condenser is 0.288 F.

Now, to calculate the new energy (E') after introducing the dielectric medium, we can use the formula E' = 1/2 * C' * V^2, where C' is the new capacitance.

Given that the relative permittivity (εr) of the dielectric medium is E-5, we can calculate the new capacitance (C').

C' = εr * C
C' = (E-5) * 0.288 F
C' = 10^-5 * 0.288 F
C' = 0.288 * 10^-5 F
C' = 2.88 * 10^-6 F

The new capacitance of the condenser with the dielectric medium is 2.88 * 10^-6 F.

Now, we can substitute the values of C' and V into the energy formula to calculate the new energy.

E' = 1/2 * C' * V^2
E' = 1/2 * (2.88 * 10^-6 F) * (120)^2
E' = 1/2 * (2.88 * 10^-6 F) * 14400
E' = 2.88 * 10^-6 F * 7200
E' = 20.736 * 10^-6 J
E' = 2.0736 * 10^-