A 2.0-microFarad capacitor is charged to 50V and then connected in parallel (positive to positive plate) with a 4.0-microFarad capacitor charged to 100V. (a) What are the final charges on the capacitors? (b) What is the potential difference across each?
To determine the final charges on the capacitors, we can apply the principle of charge conservation. When the capacitors are connected in parallel, the total charge before and after must remain the same.
(a) To find the final charge on the capacitors, we can use the formula Q = CV, where Q is the charge, C is the capacitance, and V is the potential difference.
For the 2.0-microFarad capacitor charged to 50V:
Q1 = C1 * V1 = 2.0 * 10^-6 F * 50 V = 100 * 10^-6 C = 0.1 mC
For the 4.0-microFarad capacitor charged to 100V:
Q2 = C2 * V2 = 4.0 * 10^-6 F * 100 V = 400 * 10^-6 C = 0.4 mC
Therefore, the final charges on the 2.0-microFarad capacitor and 4.0-microFarad capacitor are 0.1 mC and 0.4 mC, respectively.
(b) The potential difference across each capacitor in a parallel configuration is the same, as the positive plates of both capacitors are connected together. So, the potential difference across both capacitors will be the same as the potential difference of the 4.0-microFarad capacitor, which is 100V.