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.
We need to find the charge on and the potential difference across each capacitor.
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
The two metal spheres in Figure Q26.9 are connected by a metal wire with a switch in the middle. Initially the switch is open. Sphere 1, with the larger radius, is given a positive charge. Sphere 2, with the smaller radius, is neutral. Then the switch is closed. Afterward, sphere 1 has charge , is at potential , and the electric field strength at its surface is . The values for sphere 2 are .
a. Is larger than, smaller than, or equal to ? Explain.
b. Is larger than, smaller than, or equal to ? Explain.
c. Is larger than, smaller than, or equal to ? Explain.
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