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Chapter 19: Q14CQ (page 694)

Does the capacitance of a device depend on the applied voltage? What about the charge stored in it?

Short Answer

Expert verified

No, voltage and charge have no effect on capacitance.

Step by step solution

01

Defining Capacitance

A capacitor is a device that can retain energy, in an electrical circuit and its ability to store energy in the form of charge is known as capacitance.

02

does capacitance depend upon stored charge and the potential difference?

The capacitance of a capacitor is solely determined by its shape, size and the material used in it.

For a parallel plate capacitor, the capacitance C, is given as

C=蔚oAd

where 蔚ois the permittivity of free space, A is the area between two parallel plates and d is the distance between two parallel plates.

As, changing the applied voltage results in more charge being accumulated on the capacitor plates. Their ratio remains the same, which is the capacitance.

Therefore, the capacitance of a device does not depend on the applied voltage and the charge stored in it.

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Most popular questions from this chapter

Find the total capacitance of the combination of capacitors shown below

Construct Your Own Problem

Consider a heart defibrillator similar to that discussed in Example 19.11 . 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.

Suppose you have a \(9.00\;V\) battery, a \(2.00{\rm{ }}\mu F\) capacitor, and a \(7.40{\rm{ }}\mu F\)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.

(a) A certain parallel plate capacitor has plates of area \(4.00\;{m^2}\), separated by \(0.01\;mm\) of nylon, and stores \(0.170\;C\) of charge. What is the applied voltage? (b) What is unreasonable about this result? (c) Which assumptions are responsible or inconsistent?

An electron is to be accelerated in a uniform electric field having a strength of \({\bf{2}}.{\bf{00}} \times {\bf{1}}{{\bf{0}}^6}{\rm{ }}{\bf{V}}/{\bf{m}}\). (a) What energy in \(keV\) is given to the electron if it is accelerated through \({\bf{0}}.{\bf{400}}{\rm{ }}{\bf{m}}\)? (b) Over what distance would it have to be accelerated to increase its energy by \({\bf{50}}.{\bf{0}}{\rm{ }}{\bf{GeV}}\)?
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