Q. 57

Expert-verified
Found in: Page 740

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

What are the charge on and the potential difference across each capacitor in FIGURE ?

The potential difference on each capacitor is respectively.

And the charge on each capacitor is respectively.

See the step by step solution

Step 1: Given information

We need to find the charge on and the potential difference across each capacitor.

Step 2: Simplify

The common capacitance of the capacitor and will be

The total capacitance of the capacitor is

This means that the total charge on the system which means, in the capacitor and distributed among and will be given as

Among the two capacitors connected in parallel, this charge will be in a ratio of , the ratio of capacitances. Since the potential difference is the same for both capacitors. So,

The potential differences can be found knowing that the charge is the same for both and . We'll have

It means the potential difference across the two first capacitors will be times the potential difference of the capacitor . That is