<< Chapter < Page Chapter >> Page >
Photograph of an automated external defibrillator.
Automated external defibrillators are found in many public places. These portable units provide verbal instructions for use in the important first few minutes for a person suffering a cardiac attack.

Capacitance of a heart defibrillator

A heart defibrillator delivers 4.00 × 10 2 J of energy by discharging a capacitor initially at 1.00 × 10 4 V . What is its capacitance?

Strategy

We are given U C and V , and we are asked to find the capacitance C . We solve [link] for C and substitute.

Solution

Solving this expression for C and entering the given values yields C = 2 U C V 2 = 2 4.00 × 10 2 J ( 1.00 × 10 4 V ) 2 = 8.00 μ F .

Got questions? Get instant answers now!

Summary

  • Capacitors are used to supply energy to a variety of devices, including defibrillators, microelectronics such as calculators, and flash lamps.
  • The energy stored in a capacitor is the work required to charge the capacitor, beginning with no charge on its plates. The energy is stored in the electrical field in the space between the capacitor plates. It depends on the amount of electrical charge on the plates and on the potential difference between the plates.
  • The energy stored in a capacitor network is the sum of the energies stored on individual capacitors in the network. It can be computed as the energy stored in the equivalent capacitor of the network.

Conceptual questions

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

Got questions? Get instant answers now!

Problems

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

Got questions? Get instant answers now!

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

7.5 μ J

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

(a) What is the energy stored in the 10.0 - μ F capacitor of a heart defibrillator charged to 9.00 × 10 3 V ? (b) Find the amount of the stored charge.

a. 405 J; b. 90.0 mC

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

A 165 - μ F capacitor is used in conjunction with a dc motor. How much energy is stored in it when 119 V is applied?

1.15 J

Got questions? Get instant answers now!

Suppose you have a 9.00-V battery, a 2.00 - μ F capacitor, and a 7.40 - μ 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.

Got questions? Get instant answers now!

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 × 10 2 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. 4.43 × 10 12 F ; b. 452 V; c. 4.52 × 10 7 J ; d. no

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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 ° to 180 ° . With the dial set at 180 ° (corresponding to C = 800 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 ° . If friction is negligible, how much work is required to turn the dial from 180 ° to 0 ° ?

0.7 mJ

Got questions? Get instant answers now!
Practice Key Terms 1

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'University physics volume 2' conversation and receive update notifications?

Ask