91Ó°ÊÓ

How many \(12.5 \mu \mathrm{F}\) capacitors must be connected in parallel to store a charge of \(33.0 \mathrm{mC}\) with a potential of \(110 \mathrm{~V}\) across the capacitors?

The space between two concentric conducting spherical shells of radii \(b=1.70 \mathrm{~cm}\) and \(a=1.20 \mathrm{~cm}\) is filled with a substance of dielectric constant \(\kappa=6.91\). A potential difference \(V=73.0 \mathrm{~V}\) is applied across the inner and outer shells. Determine (a) the capacitance of the device, (b) the free charge \(q\) on the inner shell, and (c) the charge \(q^{\prime}\) induced along the surface of the inner shell.

You have two flat metal plates, each of area \(1.00 \mathrm{~m}^{2}\), with which to construct a parallel-plate capacitor. (a) If the capacitance of the device is to be \(2.00 \mathrm{~F}\), what must be the separation between the plates? (b) Could this capacitor actually be constructed?

A \(100 \mathrm{pF}\) capacitor is charged to a potential difference of \(80.0 \mathrm{~V}\), and the charging battery is disconnected. The capacitor is then connected in parallel with a second (initially uncharged) capacitor. If the potential difference across the first capacitor drops to \(35.0 \mathrm{~V}\), what is the capacitance of this second capacitor?

The plates of a spherical capacitor have radii \(37.0 \mathrm{~mm}\) and \(40.0 \mathrm{~mm}\). (a) Calculate the capacitance. (b) What must be the plate area of a parallel-plate capacitor with the same plate separation and capacitance?