Example: A spherical capacitor consists of a spherical conducting shell of radius b charge –Q concentric with a smaller conducting sphere of radius a and charge +Q. Find the capacitance of this spherical capacitor. We need to know DV to find C From Gauss’s Law Vb < Va, so 𝑉 𝑏 − 𝑉 𝑎 =− 𝑉 𝑏 − 𝑉 𝑎 E and ds are parallel cosq = 1 This is the same procedure we used to find the capacitance for the parallel plates.

3. The two capacitances are equal. Consider two capacitors, each having plate separation d. In each case, a slab of metal of thickness d/3 is inserted between the plates. In case (a), the slab is not connected to either plate. In case (b), it is connected to the upper plate. The capacitance is higher for 1. case (a). 2. case (b). 3. The two capacitances are equal. Case (a) is two capacitors in series each with separation d/3. Case (b) is a single capacitor with separation d/3. Answer: 2. The system in case (a) is equivalent to two capacitors in series, each with plate separation d/3.The system in case (b) is equivalent to a single capacitor with plate separation d/3. Adding the capacitances in case (a), and using the fact that the capacitance varies inversely with the plate separation, we find that the capacitance is larger in case (b).

Example: Use the circuit below for each of the following. Determine the equivalent capacitance of this circuit. Determine the charge stored on each capacitor. Determine the voltage across each capacitor. a)

b) & c)