Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 17: Problem 68

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 \(0.40 \mathrm{mm}\) of bakelite. What is the capacitance of this capacitor?

Short Answer

Expert verified
Solution: The capacitance of the parallel plate capacitor is approximately \(8.33 \times 10^{-11} \,\mathrm{F}\).

Step by step solution

01

Convert given quantities to standard units

Firstly, we convert given quantities to standard units. The charge given in microcoulombs should be converted to coulombs, and the plate separation given in millimeters should be converted to meters. Charge, \(Q = 0.020 \times 10^{-6} \,\mathrm{C}\). Meanwhile, Separation, \(d = 0.40 \times 10^{-3} \,\mathrm{m}\)
02

Apply the capacitance formula

Now apply the capacitance formula \(C = \frac{Q}{V}\), where \(Q\) is the charge on the plates and \(V\) is the potential difference. Substitute the given quantities and solve for capacitance, \(C\). \(C = \frac{0.020 \times 10^{-6}}{240}\)
03

Calculate the capacitance

Calculate the capacitance by dividing the charge by the potential difference. \(C = \frac{0.020 \times 10^{-6}}{240}\) \(C = 8.333 \times 10^{-11} \,\mathrm{F}\)
04

Express the result

Finally, express the capacitance to an appropriate number of significant figures and report the result in standard units: Capacitance, \(C = 8.33 \times 10^{-11} \,\mathrm{F}\)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The potential difference across a cell membrane is \(-90 \mathrm{mV} .\) If the membrane's thickness is \(10 \mathrm{nm},\) what is the magnitude of the electric field in the membrane? Assume the field is uniform.
A charge of \(+2.0 \mathrm{mC}\) is located at \(x=0, y=0\) and a charge of $-4.0 \mathrm{mC}\( is located at \)x=0, y=3.0 \mathrm{m} .$ What is the electric potential due to these charges at a point with coordinates $x=4.0 \mathrm{m}, y=0 ?$
A 4.00 - \(\mu \mathrm{F}\) air gap capacitor is connected to a \(100.0-\mathrm{V}\) battery until the capacitor is fully charged. The battery is removed and then a dielectric of dielectric constant 6.0 is inserted between the plates without allowing any charge to leak off the plates. (a) Find the energy stored in the capacitor before and after the dielectric is inserted. [Hint: First find the new capacitance and potential difference.] (b) Does an external agent have to do positive work to insert the dielectric or to remove the dielectric? Explain.
A parallel plate capacitor is composed of two square plates, $10.0 \mathrm{cm}\( on a side, separated by an air gap of \)0.75 \mathrm{mm} .$ (a) What is the charge on this capacitor when there is a potential difference of \(150 \mathrm{V}\) between the plates? (b) What energy is stored in this capacitor?
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.)
See all solutions

Recommended explanations on Physics Textbooks

Wave Optics

Read Explanation

Rotational Dynamics

Read Explanation

Force

Read Explanation

Torque and Rotational Motion

Read Explanation

Electrostatics

Read Explanation

Modern Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free