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Chapter 17: Problem 82

A parallel plate capacitor has a charge of \(0.020 \mu \mathrm{C}\) on each plate with a potential difference of \(240 \mathrm{V}\). The parallel plates are separated by 0.40 mm of air. What energy is stored in this capacitor?

Short Answer

Expert verified
Answer: The energy stored in the capacitor is \(2.40 \times 10^{-7} \mathrm{J}\).

Step by step solution

01

Calculate the capacitance

Now we will calculate the capacitance of the capacitor: \(C = \frac{0.020 \times 10^{-6} \mathrm{C}}{240 \mathrm{V}} = 8.33 \times 10^{-11} \mathrm{F}\) The capacitance of the capacitor is \(8.33 \times 10^{-11} \mathrm{F}\). #Step 2: Find the energy stored in the capacitor# Now that we have the capacitance, we can find the energy stored using the formula \(U = \frac{1}{2}CV^2\). We have: \(C = 8.33 \times 10^{-11} \mathrm{F}\) \(V = 240 \mathrm{V}\) Plug in the values, \(U = \frac{1}{2}(8.33 \times 10^{-11} \mathrm{F})(240 \mathrm{V})^2\)
02

Calculate the energy stored

Now we will calculate the energy stored in the capacitor: \(U = \frac{1}{2}(8.33 \times 10^{-11} \mathrm{F})(240 \mathrm{V})^2 = 2.40 \times 10^{-7} \mathrm{J}\) The energy stored in the capacitor is \(2.40 \times 10^{-7} \mathrm{J}\).

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Most popular questions from this chapter

The bottom of a thundercloud is at a potential of $-1.00 \times 10^{8} \mathrm{V}\( with respect to Earth's surface. If a charge of \)-25.0 \mathrm{C}$ is transferred to the Earth during a lightning strike, find the electric potential energy released. (Assume that the system acts like a capacitor-as charge flows, the potential difference decreases to zero.)
An array of four charges is arranged along the \(x\) -axis at intervals of 1.0 \(\mathrm{m}\). (a) If two of the charges are \(+1.0 \mu \mathrm{C}\) and two are \(-1.0 \mu \mathrm{C},\) draw a configuration of these charges that minimizes the potential at \(x=0 .\) (b) If three of the charges are the same, $q=+1.0 \mu \mathrm{C},\( and the charge at the far right is \)-1.0 \mu \mathrm{C},$ what is the potential at the origin?
Charges of \(-12.0 \mathrm{nC}\) and \(-22.0 \mathrm{nC}\) are separated by $0.700 \mathrm{m} .$ What is the potential midway between the two charges?
The electric potential at a distance of \(20.0 \mathrm{cm}\) from a point charge is \(+1.0 \mathrm{kV}\) (assuming \(V=0\) at infinity). (a) Is the point charge positive or negative? (b) At what distance is the potential $+2.0 \mathrm{kV} ?$
An electron is accelerated from rest through a potential difference $\Delta V\(. If the electron reaches a speed of \)7.26 \times 10^{6} \mathrm{m} / \mathrm{s},$ what is the potential difference? Be sure to include the correct sign. (Does the electron move through an increase or a decrease in potential?)
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