Additional Problems

A capacitor is made from two flat parallel plates placed 0.40 mm apart. When a charge of $0.020\text{μ}\text{C}$ 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?

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 $0\text{°}$ to $180\text{°}$. With the dial set at $180\text{°}$ (corresponding to $C=800\text{pF}$), the capacitor is connected to a 500-V source. After charging, the capacitor is disconnected from the source, and the dial is turned to $0\text{°}$. (a) What is the charge on the capacitor? (b) What is the voltage across the capacitor when the dial is set to $0\text{°}\text{?}$

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.

A parallel-plate capacitor with capacitance $5.0\text{μ}\text{F}$ 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.

Three capacitors having capacitances 8.4, 8.4, and 4.2 $\text{μ}\text{F}$ 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) On a particular day, it takes $9.60\times {10}^3\text{J}$ 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 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?