A 30-$\mu$F capacitor is charged to an unknown potential V0 and then connected across an initially uncharged 10-$\mu$F capacitor.If the final potential difference across the 10-$\mu$F capacitor is 20 V, determine V0.
A)13 V
B)27 V
C)20 V
D)29 V
E)60 V

Question

Quizplus · Accepted Answer

The total charge in the system is conserved before and after connection, therefore:

Q1 = Q2  (where Q1 is the charge on the 30-F capacitor and Q2 is the charge on the 10-F capacitor)

Using the formula for capacitance, Q=C*V, we can relate the charges to the voltages across the capacitors:

C1 * V0 = C2 * V2 + C2 * V0

where V2 is the voltage across the 10-F capacitor after connection.

We are given that V2 = 20 V and the values of the capacitors, so we can solve for V0:

(30 * 10^-6 F) * V0 = (10 * 10^-6 F) * 20 V + (10 * 10^-6 F) * V0

V0 = 27 V

A 30- μ\muμ F Capacitor Is Charged to an Unknown Potential V0 and Potential

A 30- $\mu$ F Capacitor Is Charged to an Unknown Potential V0 and Potential