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. A) 13 V B) 27 V C) 20 V D) 29 V E) 60 V

Question

Quizplus · Accepted Answer

We can apply the conservation of charge principle to solve this problem. Since the total charge on the capacitors must remain constant, we have:

Q1 + Q2 = C1*V1 + C2*V2

where Q1 and Q2 are the charges on the capacitors before they are connected, C1 and C2 are their capacitances, and V1 and V2 are their potentials (voltages) after they are connected.

Since the first capacitor is charged to an unknown potential, we can use Q1 = C1*VS1 to express its charge in terms of its capacitance and potential. Similarly, since the second capacitor is initially uncharged, we have Q2 = 0, C2 = 10 μF, and V2 = 20 V.

Substituting these values into the equation above and simplifying, we get:

C1*VS1 = 10 μF * 20 V

Solving for VS1 gives:

VS1 = 200 μC / 30 μF = 6.67 V

Therefore, the answer is choice B, 27 V.

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

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