8.3 Energy stored in a capacitor  (Page 3/4)

If you wish to store a large amount of energy in a capacitor bank, would you connect capacitors in series or parallel? Explain.

How much energy is stored in an $8.00\text{-}\text{μ}\text{F}$ capacitor whose plates are at a potential difference of 6.00 V?

A capacitor has a charge of $2.5\text{μ}\text{C}$ when connected to a 6.0-V battery. How much energy is stored in this capacitor?

How much energy is stored in the electrical field of a metal sphere of radius 2.0 m that is kept at a 10.0-V potential?

(a) What is the energy stored in the $10.0\text{-}\mu \text{F}$ capacitor of a heart defibrillator charged to $9.00\times {10}^3\text{V}$ ? (b) Find the amount of the stored charge.

In open-heart surgery, a much smaller amount of energy will defibrillate the heart. (a) What voltage is applied to the $8.00\text{-}\mu \text{F}$ capacitor of a heart defibrillator that stores 40.0 J of energy? (b) Find the amount of the stored charge.

A $165\text{-}\mu \text{F}$ capacitor is used in conjunction with a dc motor. How much energy is stored in it when 119 V is applied?

Suppose you have a 9.00-V battery, a $2.00\text{-}\mu \text{F}$ capacitor, and a $7.40\text{-}\mu \text{F}$ capacitor. (a) Find the charge and energy stored if the capacitors are connected to the battery in series. (b) Do the same for a parallel connection.

An anxious physicist worries that the two metal shelves of a wood frame bookcase might obtain a high voltage if charged by static electricity, perhaps produced by friction. (a) What is the capacitance of the empty shelves if they have area $1.00\times {10}^2{\text{m}}^2$ and are 0.200 m apart? (b) What is the voltage between them if opposite charges of magnitude 2.00 nC are placed on them? (c) To show that this voltage poses a small hazard, calculate the energy stored. (d) The actual shelves have an area 100 times smaller than these hypothetical shelves. Are his fears justified?

A parallel-plate capacitor is made of two square plates 25 cm on a side and 1.0 mm apart. The capacitor is connected to a 50.0-V battery. With the battery still connected, the plates are pulled apart to a separation of 2.00 mm. What are the energies stored in the capacitor before and after the plates are pulled farther apart? Why does the energy decrease even though work is done in separating the plates?

Suppose that the capacitance of a variable capacitor can be manually changed from 100 pF 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 $0\text{°}$ . If friction is negligible, how much work is required to turn the dial from $180\text{°}$ to $0\text{°}$ ?