"A cylindrical capacitor consists of two concentric cylinders. The inner cylinder has aradius of 5 cm and length 10 cm, while the outer cylinder has a radius of 7 cm andlength 15 cm. The space between the cylinders is filled with a dielectric material ofrelative permittivity 4. If the potential difference between the cylinders is 120 V, whatis the capacitance of the capacitor?"

Answered: Image /qna-images/answer/4f6d59a2-ad8d-4735-bc0a-c5057319202d.jpg

Answered: "A cylindrical capacitor consists of…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter20: Electric Potential And Capacitance

Section: Chapter Questions

Problem 43P

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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?
(i) Rank the following five capacitors from greatest to smallest capacitance, noting any cases of equality, (a) a 20-F capacitor with a 4-V potential difference between its plates (b) a 30-F capacitor with charges of magnitude 90 C on each plate (c) a capacitor with charges of magnitude 80 C on its plates, differing by 2 V in potential. (d) a 10-F capacitor storing energy 125 J (e) a capacitor storing energy 250 J with a 10-V potential difference (ii) Rank the same capacitors in part (i) from largest to smallest according to the potential difference between the plates, (iii) Rank the capacitors in part (i) in the order of the magnitudes of the charges on their plates, (iv) Rank the capacitors in part (i) in the order of the energy they store.
According to UE=12C(V)2 (Eq. 27.3), a greater capacitance means more energy is stored by the capacitor, but according to UE = Q2/2C (Eq. 27.2), a greater capacitance means less energy is stored. How can both of these equations be correct?
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?
The dielectric to be used in a parallel-plate capacitor has a dielectric constant of 3.60 and a dielectric strength of 1.60107 V/m. The capacitor has to have a capacitance of 1.25 nF and must be able to withstand a maximum potential difference 5.5 kV. What is the minimum area the plates of the capacitor may have?
When a Leyden jar is charged by a hand generator (Fig. 27.1, page 828), the work done by the person turning the crank is stored as electric potential energy in the jar. When a capacitor is charged by a battery, where does the electric potential energy come from?
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.
(i) A battery is attached to several different capacitors connected in parallel. Which of the following statements is true? (a) All capacitors have the same charge, and the equivalent capacitance is greater than the capacitance of any of the capacitors in the group, (b) The capacitor with the largest capacitance carries the smallest charge, (c) The potential difference across each capacitor is the same, and the equivalent capacitance is greater than any of the capacitors in the group. (d) The capacitor with the smallest capacitance carries the largest charge. (e) The potential differences across the capacitors are the same only if the capacitances are the same, (ii) The capacitors are reconnected in series, and the combination is again connected to the battery. From the same choices, choose the one that is true.
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°?
A parallel-plate capacitor is charged and then is disconnected from the battery. By what factor does the stored energy change when the plate separation is then doubled? (a) It becomes four times larger. (b) It becomes two times larger. (c) It stays the same. (d) It becomes one-half as large. (e) It becomes one-fourth as large.
An electronics technician wishes to construct a parallel plate capacitor using rutile ( = 100) as the dielectric. The area of the plates is 1.00 cm2. What is the capacitance if the rutile thickness is 1.00 mm? (a) 88.5 pF (b) 177 pF (c) 8.85 F (d) 100 F (e) 35.4 F
By what factor is the capacitance of a metal sphere multiplied if its volume is tripled? (a) 3 (b) 31/3 (c) 1 (d) 31/3 (e) 13

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