### Additional Problems

A capacitor is made from two flat parallel plates placed 0.40 mm apart. When a charge of $0.020\phantom{\rule{0.2em}{0ex}}\text{\mu}\text{C}$ is placed on the plates the potential difference between them is 250 V. (a) What is the capacitance of the plates? (b) What is the area of each plate? (c) What is the charge on the plates when the potential difference between them is 500 V? (d) What maximum potential difference can be applied between the plates so that the magnitude of electrical fields between the plates does not exceed 3.0 MV/m?

An air-filled (empty) parallel-plate capacitor is made from two square plates that are 25 cm on each side and 1.0 mm apart. The capacitor is connected to a 50-V battery and fully charged. It is then disconnected from the battery and its plates are pulled apart to a separation of 2.00 mm. (a) What is the capacitance of this new capacitor? (b) What is the charge on each plate? (c) What is the electrical field between the plates?

Suppose that the capacitance of a variable capacitor can be manually changed from 100 to 800 pF by turning a dial connected to one set of plates by a shaft, from $0\text{\xb0}$ to $180\text{\xb0}$. With the dial set at $180\text{\xb0}$ (corresponding to $C=800\phantom{\rule{0.2em}{0ex}}\text{pF}$), the capacitor is connected to a 500-V source. After charging, the capacitor is disconnected from the source, and the dial is turned to $0\text{\xb0}$. (a) What is the charge on the capacitor? (b) What is the voltage across the capacitor when the dial is set to $0\text{\xb0}\text{?}$

Earth can be considered as a spherical capacitor with two plates, where the negative plate is the surface of Earth and the positive plate is the bottom of the ionosphere, which is located at an altitude of approximately 70 km. The potential difference between Earth’s surface and the ionosphere is about 350,000 V. (a) Calculate the capacitance of this system. (b) Find the total charge on this capacitor. (c) Find the energy stored in this system.

A $4.00\text{-}\mu \text{F}$ capacitor and a $6.00\text{-}\mu \text{F}$ capacitor are connected in parallel across a 600-V supply line. (a) Find the charge on each capacitor and voltage across each. (b) The charged capacitors are disconnected from the line and from each other. They are then reconnected to each other with terminals of unlike sign together. Find the final charge on each capacitor and the voltage across each.

Three capacitors having capacitances of 8.40, 8.40, and 4.20 $\text{\mu}\text{F}$, respectively, are connected in series across a 36.0-V potential difference. (a) What is the charge on the $4.20\text{-}\text{\mu}\text{F}$ capacitor? (b) The capacitors are disconnected from the potential difference without allowing them to discharge. They are then reconnected in parallel with each other with the positively charged plates connected together. What is the voltage across each capacitor in the parallel combination?

A parallel-plate capacitor with capacitance $5.0\phantom{\rule{0.2em}{0ex}}\text{\mu}\text{F}$ is charged with a 12.0-V battery, after which the battery is disconnected. Determine the minimum work required to increase the separation between the plates by a factor of 3.

(a) How much energy is stored in the electrical fields in the capacitors (in total) shown below? (b) Is this energy equal to the work done by the 400-V source in charging the capacitors?

Three capacitors having capacitances 8.4, 8.4, and 4.2 $\text{\mu}\text{F}$ are connected in series across a 36.0-V potential difference. (a) What is the total energy stored in all three capacitors? (b) The capacitors are disconnected from the potential difference without allowing them to discharge. They are then reconnected in parallel with each other with the positively charged plates connected together. What is the total energy now stored in the capacitors?

(a) An $8.00\text{-}\mu \text{F}$ capacitor is connected in parallel to another capacitor, producing a total capacitance of $5.00\phantom{\rule{0.2em}{0ex}}\mu \text{F}$. What is the capacitance of the second capacitor? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

(a) On a particular day, it takes $9.60\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{3}\phantom{\rule{0.2em}{0ex}}\text{J}$ of electrical energy to start a truck’s engine. Calculate the capacitance of a capacitor that could store that amount of energy at 12.0 V. (b) What is unreasonable about this result? (c) Which assumptions are responsible?

(a) A certain parallel-plate capacitor has plates of area $4.00\phantom{\rule{0.2em}{0ex}}{\text{m}}^{2}$, separated by 0.0100 mm of nylon, and stores 0.170 C of charge. What is the applied voltage? (b) What is unreasonable about this result? (c) Which assumptions are responsible or inconsistent?

A prankster applies 450 V to an $80.0\text{-}\mu \text{F}$ capacitor and then tosses it to an unsuspecting victim. The victim’s finger is burned by the discharge of the capacitor through 0.200 g of flesh. Estimate, what is the temperature increase of the flesh? Is it reasonable to assume that no thermodynamic phase change happened?