Figure E$24.14$ shows a system of four capacitors, where the potential difference across ab is $50.0$ V. How much charge is stored by this combination of capacitors?

For the system of capacitors shown in Fig. E$24.16$, find the equivalent capacitance between $b$ and $c$.

A parallel-plate air capacitor is to store charge of magnitude $240.0$ pC on each plate when the potential difference between the plates is $42.0$ V.

(a) If the area of each plate is $6.80$ cm², what is the separation between the plates?

(b) If the separation between the two plates is double the value calculated in part (a), what potential difference is required for the capacitor to store charge of magnitude $240.0$ pC on each plate?

Figure E$24.14$ shows a system of four capacitors, where the potential difference across ab is $50.0$ V. How much charge is stored in each of the $10.0$-$\mu$F and the $9.0$-$\mu$F capacitors?

In Fig. E$24.20$, $C_1=6.00$ $\mu$F, $C_2=3.00$ $\mu$F, and $C_3=5.00$ $\mu$F. The capacitor network is connected to an applied potential $V_{ab}$.

(a) After the charges on the capacitors have reached their final values, the charge on $C_2$ is $30.0$ mC. What are the charges on capacitors $C_1$ and $C_3$?

(b) What is the applied voltage $V_{ab}$?

A capacitor is made from two hollow, coaxial, iron cylinders, one inside the other. The inner cylinder is negatively charged and the outer is positively charged; the magnitude of the charge on each is $10.0$ pC. The inner cylinder has radius $0.50$ mm, the outer one has radius $5.00$ mm, and the length of each cylinder is $18.0$ cm.

(a) What is the capacitance?

(b) What applied potential difference is necessary to produce these charges on the cylinders?

A spherical capacitor contains a charge of $3.30$ nC when connected to a potential difference of $220$ V. If its plates are separated by vacuum and the inner radius of the outer shell is $4.00$ cm, calculate: (a) the capacitance; (b) the radius of the inner sphere; (c) the electric field just outside the surface of the inner sphere.