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Chapter 23: Problem 55

A parallel-plate capacitor has plates with area \(50 \mathrm{cm}^{2}\) separated by \(25 \mu \mathrm{m}\) of polyethylene. Find its (a) capacitance and (b) working voltage.

Short Answer

Expert verified
The capacitance of the capacitor is 37.4 pF and its working voltage is 500 kV.

Step by step solution

01

Convert units

Start by converting the given units into SI units. The area \(A\) should be in m², so we convert it from cm² to m². And the separation \(d\) should be in m, so we convert it from μm to m.
02

Calculate The Capacitance

To calculate the capacitance, we will use the formula \(C = \frac{\varepsilon_{0} \varepsilon_{r} A}{d}\). Where \(\varepsilon_{0} = 8.85 \times 10^{-12} F/m\), \(\varepsilon_{r} = 2.3\) for polyethylene, \(A\) is the area we obtained from part 1 and \(d\) is the separation we obtained from part 1.
03

Working Voltage

The breakdown field strength of polyethylene is \(E = 20 MV/m\), we will rearrange the formula \(E = \frac{V}{d}\) to solve for \(V\).
04

Calculate The Working Voltage

Substitute the given values into the formula to find the working voltage.

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Most popular questions from this chapter

Charge is spread over the surface of a balloon, which is then allowed to expand. What happens to the energy of the electric field?

You're evaluating a new hire in your company's engineering department. Together you're working on a circuit where a \(0.1-\mu \mathrm{F}\) \(50-\mathrm{V}\) capacitor is in series with a \(0.2-\mu \mathrm{F}, 200-\mathrm{V}\) capacitor. The new engineer claims you can safely put \(250 \mathrm{V}\) across the combination. What do you say?

A solid sphere contains a uniform volume charge density. What fraction of the total electrostatic energy of this configuration is contained within the sphere?

Two widely separated 4.0 -mm-diameter water drops each carry 15 nC. Assuming all charge resides on the drops' surfaces, find the change in electrostatic potential energy if they're brought together to form a single spherical drop.

Is a force needed to hold the plates of a charged capacitor in place? Explain.
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