A 30-μF capacitor is charged to an unknown potential V0 and then connected across an initially uncharged 10-μF capacitor. If the final potential difference across the 10-μF capacitor is 20 V, determine V0.

Question

Quizplus · Accepted Answer

We can start by using the principle of conservation of charge, which states that the total charge in a system must remain constant. Since the capacitors are connected in parallel, they have the same final potential difference of 20 V. Let Q1 and Q2 be the charges on the 30-μF and 10-μF capacitors, respectively, after they are connected. Then:

Q1 = C1V and Q2 = C2V

where V is the final potential difference of 20 V. The total charge in the system is:

Q = Q1 + Q2 = C1V + C2V = (C1 + C2)V

Using the conservation of charge, we know that Q1 = Q2. Thus:

C1V = C2V
V = C2/C1 * V0

Substituting the given capacitor values, we get:

20 V = (10 μF)/(30 μF) * V0
V0 = 60 V/3 = 20 V * 3 = 60 V/3

Therefore, the initial potential across the 30-μF capacitor is V0 = 20 V * 3 = 60 V/3 = 27 V (rounded to the nearest integer), which corresponds to choice B.

A 30-μF Capacitor Is Charged to an Unknown Potential V0