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Chapter 21: Problem 53

To what potential should you charge a \(1.0 \mu \mathrm{F}\) capacitor to store \(1.0 \mathrm{J}\) of energy?

Short Answer

Expert verified
The potential to which a \(1.0 \mu \mathrm{F}\) capacitor should be charged to store \(1.0 \mathrm{J}\) of energy is approximately \(1414.21 \mathrm{V}\).

Step by step solution

01

Identify Given Values

From the question, the capacitance \(C\) of the capacitor is given as \(1.0 \mu \mathrm{F}\) (or \(1.0 \times 10^{-6} \mathrm{F}\)) and the energy \(E\) to be stored in the capacitor is given as \(1.0 \mathrm{J}\).
02

Apply the Energy-Capacitance-Potential Relation

We need to rearrange the formula to find the potential difference \(V\). That results in \(V = \sqrt{\frac{2E}{C}}\).
03

Substitute Known Values into the Equation

Substituting the given values into the equation gives \(V = \sqrt{\frac{2 \times 1.0 \mathrm{J}}{1.0 \times 10^{-6} \mathrm{F}}}\).
04

Solve the Equation

Calculate the right-hand side of the equation to get the desired potential difference \(V = 1414.21 \mathrm{V}\).

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Most popular questions from this chapter

The capacity of a battery to deliver charge, and thus power, decreases with temperature. The same is not true of capacitors. For sure starts in cold weather, a truck has a 500 F capacitor alongside a battery. The capacitor is charged to the full \(13.8 \mathrm{V}\) of the truck's battery. How much energy does the capacitor store? How does the energy density of the \(9.0 \mathrm{kg}\) capacitor system compare to the \(130,000 \mathrm{J} / \mathrm{kg}\) of the truck's battery?

A proton with an initial speed of \(800,000 \mathrm{m} / \mathrm{s}\) is brought to rest by an electric field. a. Did the proton move into a region of higher potential or lower potential? b. What was the potential difference that stopped the proton? c. What was the initial kinetic energy of the proton, in electron Volts?

Moving a charge from point A, where the potential is \(300 \mathrm{V}\), to point \(\mathrm{B},\) where the potential is \(150 \mathrm{V},\) takes \(4.5 \times 10^{-4} \mathrm{J}\) of work. What is the value of the charge?

Two uncharged metal spheres, spaced \(15.0 \mathrm{cm}\) apart, have a capacitance of 24.0 pF. How much work would it take to move \(12.0 \mathrm{nC}\) of charge from one sphere to the other?

In proton-beam therapy, a high-energy beam of protons is fired at a tumor. The protons come to rest in the tumor, depositing their kinetic energy and breaking apart the tumor's DNA, thus killing its cells. For one patient, it is desired that \(0.10 \mathrm{J}\) of proton energy be deposited in a tumor. To create the proton beam, the protons are accelerated from rest through a \(10 \mathrm{MV}\) potential difference. What is the total charge of the protons that must be fired at the tumor to deposit the required energy?
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