If a voltage is applied across a capacitor by connecting the capacitor to a bat- tery with conducting wires as in Fig. 17–14, charge flows from the battery to each of the two plates: one plate acquires a negative charge, the other an equal amount of positive charge. Each battery terminal and the plate of the capacitor connected to it are at the same potential; hence the full battery voltage appears across the capacitor. For a given capacitor, it is found that the amount of charge Q acquired by each plate is proportional to the magnitude of the potential difference V between the plates: Q = CV. (17–7) The constant of proportionality, C, in Eq. 17–7 is called the capacitance of the capacitor. The unit of capacitance is coulombs per volt, and this unit is called a farad (F). Common capacitors have capacitance in the range of 1 pF (picofarad = 10 12F) to 10° µF (microfarad = 10 F). The relation, Eq. 17-7, was first suggested by Volta in the late eighteenth century. In Eq. 17–7 and from now on, we will use simply V (in italics) to represent a potential difference, such as that produced by a battery, rather than Vpa, AV, or V - Va, as previously.

If a voltage is applied across a capacitor by connecting the capacitor to a bat- tery with conducting wires as in Fig. 17–14, charge flows from the battery to each of the two plates: one plate acquires a negative charge, the other an equal amount of positive charge. Each battery terminal and the plate of the capacitor connected to it are at the same potential; hence the full battery voltage appears across the capacitor. For a given capacitor, it is found that the amount of charge Q acquired by each plate is proportional to the magnitude of the potential difference V between the plates: Q = CV. (17–7) The constant of proportionality, C, in Eq. 17–7 is called the capacitance of the capacitor. The unit of capacitance is coulombs per volt, and this unit is called a farad (F). Common capacitors have capacitance in the range of 1 pF (picofarad = 10 12F) to 10° µF (microfarad = 10 F). The relation, Eq. 17-7, was first suggested by Volta in the late eighteenth century. In Eq. 17–7 and from now on, we will use simply V (in italics) to represent a potential difference, such as that produced by a battery, rather than Vpa, AV, or V - Va, as previously.

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter8: Capacitance

Section: Chapter Questions

Problem 49P: Suppose that the capacitance of a variable capacitor can be manually changed from 100 pF to 800 pF...

See similar textbooks

Similar questions

Check Your Understanding Repeat the calculations of Example 8.10 for the case in which the battery remains connected while the dielectric is placed in the capacitor.
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°?
Check Your Understanding The capacitance of a parallel-plate capacitor is 2.0 pF. If the area of each plate is 2.4 cm2, what is the plate separation?
Check Your Understanding When a cylindrical capacitor is given a charge of 0.500 nC, a potential difference of 20.0 V is measured between the cylinders, (a) What is the capacitance of this system? (b) If the cylinders are 1.0 m long, what is the ratio of their radii?
Check Your Understanding Is the electrical potential energy of two point charges positive or negative if the charges are of the same sign? Opposite signs? How does this relate to the work necessary to bring the charges into proximity from infinity?
Would electric potential energy be meaningful if the electric field were not conservative?
Check Your Understanding Continuing with Example 8.12, show that when the battery is connected across the plates the energy stored in dielectric-filled capacitor is U=kU0 (larger than the energy U0 of an empty capacitor kept at the same voltage). Compare this result with the result U=U0/K found previously for an isolated, charged capacitor.
Check Your Understanding Determine the net capacitance C of each network of capacitors shown below. Assume the C1= 1.0 pF, C2=2.0pF, C3=4.0pF, and C4=5.0 pF. Find the charge on each capacitor, assuming there is a potential difference of 12.0 V across each network.
Check Your Understanding What are the equipotential surfaces for an infinite line charge?
Check Your Understanding What is the potential on the axis of a nonuniform ring of charge, where the charge density is ()=cos ?
Check Your Understanding The potential difference across a 5.0-pF capacitor is 0.40 V. (a) What is the energy stored in this capacitor? (b) The potential difference is now increased to 1.20 V. By what factor is the stored energy increased?
Check Your Understanding The radius of the outer sphere of a spherical capacitor is five times the radius of its inner shell. What are the dimensions of this capacitor if its capacitance is 5.00 pF?