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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

A defibrillator is used to restart a person's heart after it stops beating. Energy is delivered to the heart by discharging a capacitor through the body tissues near the heart. If the capacitance of the defibrillator is $9 \mu \mathrm{F}\( and the energy delivered is to be \)300 \mathrm{J},$ to what potential difference must the capacitor be charged?
A parallel plate capacitor has a capacitance of \(1.20 \mathrm{nF}\) and is connected to a \(12-\mathrm{V}\) battery. (a) What is the magnitude of the charge on each plate? (b) If the plate separation is doubled while the plates remain connected to the battery, what happens to the charge on each plate and the electric field between the plates?
Point \(P\) is at a potential of \(500.0 \mathrm{kV}\) and point \(S\) is at a potential of \(200.0 \mathrm{kV} .\) The space between these points is evacuated. When a charge of \(+2 e\) moves from \(P\) to \(S\), by how much does its kinetic energy change?
The nucleus of a helium atom contains two protons that are approximately 1 fm apart. How much work must be done by an external agent to bring the two protons from an infinite separation to a separation of \(1.0 \mathrm{fm} ?\)
A parallel plate capacitor is charged by connecting it to a \(12-V\) battery. The battery is then disconnected from the capacitor. The plates are then pulled apart so the spacing between the plates is increased. What is the effect (a) on the electric field between the plates? (b) on the potential difference between the plates?
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