A parallel plate capacitor as a materials characterisation tool

Error

There was an error loading the page.

Contributors

Feedback

From users who are members of ENG1003 20-21 :

Jon Goss

said

Ready to use

5 years, 3 months ago

History

○

Jon Goss 4 years, 1 month ago

Published this.

○

Jon Goss 5 years, 3 months ago

Gave some feedback: Ready to use

○

Jon Goss 5 years, 4 months ago

Gave some feedback: Needs to be tested

○

Jon Goss 5 years, 4 months ago

Created this as a copy of Characteristics of a parallel plate capacitor..

There is only one version of this question that you have access to.

There are 5 other versions that do you not have access to.

Question statement

This question focuses upon the permittivity of materials in parallel plate capacitors.

A parallel plate capacitor has circular plates of radius {radiusmm} mm and the distance between the plates, $d$ , is {distanceu} μm. The capacitor is connected to a battery indicated as {battery} V.

Discs that fill the space between the plates comprised from various materials can be placed between the electrodes and the energy stored recorded.

When providing numerical answers you may express them using scientific notation. Express values to four significant figures and use the values of physical constants as provided in the course notes.

Give any introductory information the student needs.

			Name	Type	Generated Value

area	number	0.0002010619
battery	number	3
battery2	number	2.5
distance	number	0.00013
distanceu	number	130
energya	number	0.000000016
energyan	number	16
eps0	decimal	dec("0.000000000008854")
epsra	decimal	dec("2.596458926526658999749243017235260217631e+2")
radius	number	0.008
radiusmm	number	8

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
pi radius^2

JME function reference

Description

Area of the plates in m^2.

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `number`

0.0002010619

← Depends on:

radius

→ Used by:

epsra

Parts

Energy Gap-fill
1. Gap formula Mathematical expression
  Add
2. Gap CD Choose one from a list
  Add
3. Gap CU Choose one from a list
  Add
4. Gap VD Choose one from a list
  Add
5. Gap VU Choose one from a list
  Add
Relative permittivity of material A Gap-fill
1. Gap eps_r Number entry
  Add
Material B Information only
Error Gap-fill
1. Gap Choose one from a list
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

State the formula for the energy stored in an ideal parallel plate capacitor as a function of $C$ and $V$ . Stating the meaning of all symbols and providing suitable units.

Energy stored = formula

$C$ is the CD with units CU

$V$ is the VD with units VU

Advice

The first step is to note that the energy stored is

$\displaystyle {CV^2\over2},$

and that

$\displaystyle C={\varepsilon A\over d},$

where $C$ is the capacitance (F), $V$ is the potential difference between the two plates (volts), $\varepsilon$ is the permittivity (F/m) of the medium between the plates of area $A$ (m $^2$ ) and separation $d$ (m).

The relative permittivity of the medium is obtainable:

$\displaystyle {\rm energy~stored}={1\over 2}CV^2={1\over2}{\varepsilon_0\varepsilon_r A\over d}V^2\Rightarrow \varepsilon_r={2 d \times {\rm stored~energy}\over \varepsilon_0 AV^2}$ .

We have all the quantities so $\varepsilon_r$ can be obtained.

Noting that the relative permittivity is inversely proportional to the voltage (squared), if the voltage of the battery is lower than indicated then the permittivity is higher than previously estimated, and so therefore is the capacitance.

Give a worked solution to the whole question.

URL

Text alternative

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Choose one from a list
Choose one from a list		Hasn't run yet
Choose one from a list
Choose one from a list		Hasn't run yet
Choose one from a list
Choose one from a list		Hasn't run yet
Choose one from a list
Choose one from a list		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Information only
Gap-fill
Gap-fill		Hasn't run yet
Choose one from a list
Choose one from a list		Hasn't run yet

This question is used in the following exams:

Mid term test 2018/19 by Jon Goss in EEE1001 & PHY1023.
All electromag by Jon Goss in EEE1001 & PHY1023.
TEST by Jon Goss in Jon's workspace.
PHY1036 5pc part 1 by Jon Goss in NCL PHY1036.
PHY1024 Assessment 1 by Aleksey Kozikov in NCL PHY1024.
Assignment 2 - PHY1024 by Shweta Sharma in NCL PHY1024.

Loading...

Error

A parallel plate capacitor as a materials characterisation tool

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Jon Goss 4 years, 1 month ago

Jon Goss 5 years, 3 months ago

Jon Goss 5 years, 4 months ago

Jon Goss 5 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: `number`

Parts

Gap-fill

Loading...

Error

A parallel plate capacitor as a materials characterisation tool

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Jon Goss 4 years, 1 month ago

Jon Goss 5 years, 3 months ago

Jon Goss 5 years, 4 months ago

Jon Goss 5 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`