Two identical capacitors are connected in parallel and each acquires a charge Q₀ when connected to a source of voltage V₀. The voltage source is disconnected and then a dielectric (K = 3.6) is inserted to fill the space between the plates of one of the capacitors. Determine the voltage now across each capacitor.

The long cylindrical capacitor shown in Fig. 24–37 consists of four concentric cylinders, with respective radii R_a, R_b, R_c and R_d. The cylinders b and c are joined by metal strips. Determine the capacitance per unit length of this arrangement. (Assume equal and opposite charges are placed on the innermost and outermost cylinders.)

What is the capacitance of a pair of circular plates with a radius of 5.0 cm separated by 2.3 mm of mica?

A parallel-plate capacitor with plate area 2.0 cm² and air-gap separation 0.50 mm is connected to a 12-V battery, and fully charged. The battery is then disconnected. What is the charge on the capacitor?

(I) The two plates of a capacitor hold +3500 μC and -3500μC of charge, respectively, when the potential difference is 960 V. What is the capacitance?

A general rule for estimating the capacitance C of an isolated conducting sphere with radius r is C (in pF) ≈ r (in cm). That is, the numerical value of C in pF is about the same as the numerical value of the sphere’s radius in cm. Justify this rule.

Capacitors can be used as “electric charge counters.” Consider an initially uncharged capacitor of capacitance C with its bottom plate grounded and its top plate connected to a source of electrons. If N electrons flow onto the capacitor’s top plate, show that the resulting potential difference V across the capacitor is directly proportional to N.

Capacitors can be used as “electric charge counters.” Consider an initially uncharged capacitor of capacitance C with its bottom plate grounded and its top plate connected to a source of electrons. Assume a voltage-measuring device can accurately resolve voltage changes of about 1 mV. What value of C would be necessary to resolve the arrival of an individual electron?

In the dynamic random access memory (DRAM) of a cell phone, each memory cell contains a capacitor for charge storage. Each of these cells represents a single binary-bit value of “1” when its 25-fF capacitor (1 fF = 10^-15 F )is charged at 0.6 V, or “0” when uncharged at 0 V. When fully charged, how many excess electrons are on a cell capacitor’s negative plate?