19.7 Energy stored in capacitors  (Page 3/4)

Consider a parallel plate capacitor, with no dielectric material, attached to a battery with a fixed voltage. What happens when a dielectric is inserted into the capacitor?

1. Nothing changes, except now there is a dielectric in the capacitor.
2. The energy in the system decreases, making it very easy to move the dielectric in.
3. You have to do work to move the dielectric, increasing the energy in the system.
4. The reversed polarity destroys the battery.

Consider a parallel plate capacitor with no dielectric material. It was attached to a battery with a fixed voltage to charge up, but now the battery has been disconnected. What happens to the energy of the system and the dielectric material when a dielectric is inserted into the capacitor?

What happens to the energy stored in a circuit as you increase the number of capacitors connected in parallel? Series?

1. increases, increases
2. increases, decreases
3. decreases, increases
4. decreases, decreases

What would the capacitance of a capacitor with the same total internal energy as the car battery in Example 19.1 have to be? Can you explain why we use batteries instead of capacitors for this application?

Consider a parallel plate capacitor with metal plates, each of square shape of 1.00 m on a side, separated by 1.00 mm. What is the energy of this capacitor with 3.00×10 ³ V applied to it?

1. 3.98×10 ^-2 J
2. 5.08×10 ¹⁴ J
3. 1.33×10 ^-5 J
4. 1.69×10 ¹¹ J

Consider a parallel plate capacitor with metal plates, each of square shape of 1.00 m on a side, separated by 1.00 mm. What is the internal energy stored in this system if the charge on the capacitor is 30.0 µC?

Consider a parallel plate capacitor with metal plates, each of square shape of 1.00 m on a side, separated by 1.00 mm. If the plates grow in area while the voltage is held fixed, the capacitance ___ and the stored energy ___.

1. decreases, decreases
2. decreases, increases
3. increases, decreases
4. increases, increases

Consider a parallel plate capacitor with metal plates, each of square shape of 1.00 m on a side, separated by 1.00 mm. What happens to the energy of this system if the area of the plates increases while the charge remains fixed?

How does the energy contained in a charged capacitor change when a dielectric is inserted, assuming the capacitor is isolated and its charge is constant? Does this imply that work was done?

What happens to the energy stored in a capacitor connected to a battery when a dielectric is inserted? Was work done in the process?

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

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

A $1\text{65 µF}$ capacitor is used in conjunction with a motor. How much energy is stored in it when 119 V is applied?

Suppose you have a 9.00 V battery, a $\text{2.00 μF}$ capacitor, and a $\text{7.40 μF}$ 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.

A nervous physicist worries that the two metal shelves of his 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 $1.00\times {\text{10}}^{\text{2}}{\text{m}}^{\text{2}}$ 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.

Show that for a given dielectric material the maximum energy a parallel plate capacitor can store is directly proportional to the volume of dielectric ( $\text{Volume =}A·d$ ). Note that the applied voltage is limited by the dielectric strength.

Construct Your Own Problem

Consider a heart defibrillator similar to that discussed in [link] . Construct a problem in which you examine the charge stored in the capacitor of a defibrillator as a function of stored energy. Among the things to be considered are the applied voltage and whether it should vary with energy to be delivered, the range of energies involved, and the capacitance of the defibrillator. You may also wish to consider the much smaller energy needed for defibrillation during open-heart surgery as a variation on this problem.

Unreasonable Results

(a) On a particular day, it takes $9.60\times {\text{10}}^{\text{3}}\text{J}$ of electric 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?