Problem: The plates of a parallel plate capacitor are given charges 4Q and -2Q. The capacitor is then connected across an uncharged capacitor of the same capacitance C. Find the final potential difference between the plates of the first capacitor.

Solution:

Step 1: Find the initial potential difference between the plates of the first capacitor

The potential difference between the plates of a capacitor is given by the formula:

V = Q/C

where Q is the charge on the capacitor and C is the capacitance. Therefore, the initial potential difference between the plates of the first capacitor is:

V1 = (4Q - (-2Q))/C

V1 = 6Q/C

Step 2: Find the total charge on the two capacitors when they are connected in parallel

When two capacitors are connected in parallel, the total charge on the two capacitors is conserved. Therefore, the total charge on the two capacitors when they are connected in parallel is:

Qt = Q1 + Q2

where Q1 and Q2 are the charges on the two capacitors. In this case, Q1 = 4Q and Q2 = -2Q. Therefore, the total charge on the two capacitors is:

Qt = 4Q - 2Q = 2Q

Step 3: Find the final potential difference between the plates of the first capacitor

When the two capacitors are connected in parallel, the potential difference between the plates of the first capacitor will decrease. The final potential difference between the plates of the first capacitor is given by the formula:

Vf = Qt/C

where Qt is the total charge on the two capacitors and C is the capacitance of each capacitor. Therefore, the final potential difference between the plates of the first capacitor is:

Vf = 2Q/C

Step 4: Find the change in potential difference between the plates of the first capacitor

The change in potential difference between the plates of the first capacitor is given by the formula:

ΔV = Vf - V1

Substituting the values of Vf and V1 obtained in steps 3 and 1 respectively, we get:

ΔV = (2Q/C) - (6Q/C)

ΔV = -4Q/C

Therefore, the final potential difference between the plates of the first capacitor is -4Q/C.

Conclusion: The final potential difference between the plates of the first capacitor is found to be -4Q/C when it is connected across an uncharged capacitor of the same capacitance C.

Q/2c