A 30-μF capacitor is charged to 40 V and then connected across an initially uncharged 20-μF capacitor. What is the final potential difference across the 30-μF capacitor?
A) 15 V
B) 24 V
C) 18 V
D) 21 V
E) 40 V

Question

Quizplus · Accepted Answer

When two capacitors are connected in parallel, the charge is redistributed between them, but the total charge is conserved. The initial charge on the 30-μF capacitor is $Q = CV = 30 \times 10^{-6} \, \text{F} \times 40 \, \text{V} = 1200 \times 10^{-6} \, \text{C}$. When this charge is redistributed between the 30-μF and 20-μF capacitors, the total capacitance becomes $30 + 20 = 50 \, \mu\text{F}$. The final voltage across both capacitors (which is the same since they are in parallel) can be found by $V = \frac{Q}{C_{\text{total}}} = \frac{1200 \times 10^{-6} \, \text{C}}{50 \times 10^{-6} \, \text{F}} = 24 \, \text{V}$.

A 30-μF Capacitor Is Charged to 40 V and Then