Question

Capacitors C1=10μF and C2=20μF are each charged to 14 V , then disconnected from the battery without changing the charge on the capacitor plates. The two capacitors are then connected in parallel, with the positive plate of C1connected to the negative plate of C2 and vice versa.

(a) Afterward, what is the charge on each capacitor?

(b) What is the potential difference across each capacitor?

Answer 1

Concepts and reason

The concepts used to solve this problem are charge, voltage, and parallel combination of capacitors.

Use the concepts of charge, voltage, and parallel combination of capacitors to find the new charge on the capacitor after connecting it in a parallel combination.

Use the concept of voltage to find the potential difference across each capacitor.

Fundamentals

The expression for capacitance is as follows:

Here, the charge is , voltage is , and capacitance is .

The expression for the total capacitance in a parallel combination is given below:

Here, is the total capacitance and , , are the capacitances.

The expression for the charge on a capacitor is given below:

$Q=CV $

(a)

The expression for the charge on a capacitor is given below:

$Q=CV $

The expression for the charge on a capacitor is given below:

Here, is the charge on a capacitor .

Substitute for and for .

The expression for the charge on a capacitor is given below:

Here, is the charge on a capacitor .

Substitute for and for .

When the capacitor is connected in parallel combination with the negative plate of one connected to the positive plate of the other, the net charge stored is equal to the charge difference between the capacitors.

Therefore

Substitute for and for .

The expression for equivalent capacitance in parallel combination is given below:

The expression for capacitances and in a parallel combination is given below:

Substitute for and for .

The expression for the equivalent capacitance is as follows:

Substitute for and for .

The expression for the new charge on a capacitor after connecting it in a parallel combination is given below:

Here, is the new charge on a capacitor after connecting the capacitors in a parallel combination.

Substitute for and for .

The expression for the charge on a capacitor after connecting it in a parallel combination is given below:

Here, is the new charge on a capacitor after connecting it in a parallel combination.

Substitute for and for .

(b)

The expression for the charge on a capacitor is given below:

When the capacitors are connected in a parallel combiantion, the voltage across each capacitor is the same.

Therefore, the potential difference across each capacitor is .

Ans: Part a

The new charges on capacitors and after connecting them in a parallel combination are and , respectively.

Part b

The potential difference across each capacitor is .