Solving the Two Capacitor Problem: Calculating Final Potential Difference

[Vibhor]

Homework Statement

Two capacitors ##C_1## and ##C_2## (where ##C_1 > C_2##) are charged to the same initial potential difference ##V_i##
, but with opposite polarity. The charged capacitors are removed from the battery, and their plates are connected as shown in Figure a. The switches ##S_1## and ##S_2## are then closed, as shown in Figure b. Find the final potential difference
##V_f## between a and b after the switches are closed

Homework Equations

The Attempt at a Solution

Let V_f be final potential difference.

## V_f = \frac{Q_{1f}}{C_1} = \frac{Q_{2f}}{C_2}##
## Q_1-Q_2 = Q_{1f}+Q_{2f}##
## Q_1-Q_2 = Q_{1f}+\frac{C_2}{C_1}Q_{1f}##
## C_1V_i-C_2V_i = \frac{C_1+C_2}{C_1}Q_{1f}##

## V_f = \frac{C_1-C_2}{C_1+C_2}V_i##

Is this correct ?

 

[ehild]

Let V_f be final potential difference.

## V_f = \frac{Q_{1f}}{C_1} = \frac{Q_{2f}}{C_2}##
## Q_1-Q_2 = Q_{1f}+Q_{2f}##
## Q_1-Q_2 = Q_{1f}+\frac{C_2}{C_1}Q_{1f}##
## C_1V_i-C_2V_i = \frac{C_1+C_2}{C_1}Q_{1f}##

## V_f = \frac{C_1-C_2}{C_1+C_2}V_i##

Is this correct ?

Yes.

ehild

 

[Vibhor]

Many thanks ehild :)