A coaxial cable used in a transmission line has an inner radius of 0.14 mm and an outer radius of 0.67 mm. Calculate the capacitance- per meter for the cable. Assume that the space between the conductors is filled with a material with a dielectric constant of 3.8. Number i Units

A coaxial cable used in a transmission line has an inner radius of 0.14 mm and an outer radius of 0.67 mm. Calculate the capacitance- per meter for the cable. Assume that the space between the conductors is filled with a material with a dielectric constant of 3.8. Number i Units

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter8: Capacitance

Section: Chapter Questions

Problem 38P: A 40-pF capacitor is charged to a potential difference of 500 V. Its terminals are then connected to...

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You are working in a laboratory, using very sensitive measurement equipment. Your supervisor has explained that the equipment is also very sensitive to electrical discharge from human operators. Specification tables for the equipment indicate that an electrical discharge providing even a very small amount of energy of 250 J is enough to damage the equipment. Your supervisor wants to install an apparatus that will be used to remove the electrical charge from individuals bodies before they touch the equipment. To do this, she asks you to estimate (a) the capacitance of the human body and determine (b) the charge on the body and (c) the electric potential of the body, relative to a point infinitely far away, corresponding to the energy transfer that will damage the equipment.
If you have ever tried to hang a picture or a mirror, you know it can be difficult to locate a wooden stud in which to anchor your nail or screw. A carpenters stud finder is a capacitor with its plates arranged side by side instead of facing each other as shown in Figure 20.32. When the device is moved over a stud, does the capacitance (a) increase or (b) decrease?
A variable air capacitor used in a radio tuning circuit is made of N semicircular plates, each of radius R and positioned a distance d from its neighbors, to which it is electrically connected. As shown in Figure P20.38, a second identical set of plates is enmeshed with the first set. Each plate in the second set is halfway between two plates of the first set. The second set can rotate as a unit. Determine the capacitance as a function of the angle of rotation , where = 0 corresponds to the maximum capacitance. Figure P20.38
Referring to Figure CQ21.4, describe what happens to the light-bulb after the switch is closed. Assume the capacitor has a large capacitance and is initially uncharged. Also assume the light illuminates when connected directly across the battery terminals.
The immediate cause of many deaths is ventricular fibrillation, which is an uncoordinated quivering of the heart. An electric shock to the chest can cause momentary paralysis of the heart muscle, after which the heart sometimes resumes its proper beating. One type of defibrillator (chapter-opening photo, page 777) applies a strong electric shock to the chest over a time interval of a few milliseconds. This device contains a capacitor of several microfarads, charged to several thousand volts. Electrodes called paddles are held against the chest on both sides of tire heart, and the capacitor is discharged through the patient's chest. Assume an energy of 300 J is to be delivered from a 30.0-F capacitor. To what potential difference must it be charged?
Unreasonable Results (a) On a particular day, it takes 9.60 103 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?
Some physical systems possessing capacitance continuously distributed over space can be modeled as an infinite array of discrete circuit elements. Examples are a microwave waveguide and the axon of a nerve cell. To practice analysis of an infinite array, determine the equivalent capacitance C between terminals X and Y of the infinite set of capacitors represented in Figure P25.47. Each capacitor has capacitance C0. Suggestions: Imagine that the ladder is cut at the line AB and note that the equivalent capacitance of the infinite section to the right of AB is also C.
In places such as hospital operating rooms or factories for electronic circuit boards, electric sparks must be avoided. A prison standing on a grounded floor and touching nothing else can typically have a body capacitance of 150 pF, in parallel with a foot capacitance of 80.0 pF produced by the dielectric soles of his or her shoes. The person acquires static electric charge from interactions with Ills or her surroundings. The static charge flows to ground through the equivalent resistance of the two shoe soles in parallel with each other. A pair of rubber-soled street shoes can present an equivalent resistance of 5.00 103 M. A pair of shoes with special static-dissipative soles can have an equivalent resistance of 1.00 M. Consider the persons body and shoes as forming an RC circuit with the ground. (a) How long does it take the rubber-soled shoes to reduce a persons potential from 3.00 103 V to 100? (b) How long does it take the static-dissipative shoes to do the same thing?
Earth can be considered as a spherical capacitor with two plates, where the negative plate is the surface of Earth and the positive plate is the bottom of the ionosphere, which is located at an altitude of approximately 70 km. The potential difference between Earth’s surface and the ionosphere is about 350,000 V. (a) Calculate the capacitance of this system, (b) Find the total charge on this capacitor, (c) Find the energy stored in this system.
A capacitor is constructed from two square, metallic plates of sides and separation d. Charges +Q and Q are placed on the plates, and the power supply is then removed. A material of dielectric constant K is inserted a distance x into the capacitor as shown in Figure P20.85. Assume d is much smaller than x. (a) Find the equivalent capacitance of the device. (b) Calculate the energy stored in the capacitor. (c) Find the direction and magnitude of the force exerted by the plates on the dielectric. (d) Obtain a numerical value for the force when x = /2, assuming = 5.00 cm, d = 2.00 mm, the dielectric is glass ( = 4.50), and the capacitor was charged to 2.00 103 V before the dielectric was inserted. Suggestion: The system can be considered as two capacitors connected in parallel. Figure P20.85
A 40-pF capacitor is charged to a potential difference of 500 V. Its terminals are then connected to those of an uncharged 10-pF capacitor. Calculate: (a) the original charge on the 40-pF capacitor; (b) the charge on each capacitor after the connection is made; and (c) the potential difference across the plates of each capacitor after the connection.
A Pairs of parallel wires or coaxial cables are two conductors separated by an insulator, so they have a capacitance. For a given cable, the capacitance is independent of the length if the cable is very long. A typical circuit model of a cable is shown in Figure P27.87. It is called a lumped-parameter model and represents how a unit length of the cable behaves. Find the equivalent capacitance of a. one unit length (Fig. P27.87A), b. two unit lengths (Fig. P27.87B), and c. an infinite number of unit lengths (Fig. P27.87C). Hint: For the infinite number of units, adding one more unit at the beginning does not change the equivalent capacitance.