Time varying current - Faraday's law - Numbas at mathcentre.ac.uk

Error

There was an error loading the page.

Contributors

Jon Goss

Feedback

From users who are members of EEE1001 & PHY1023 :

Jon Goss

said

Ready to use

5 years, 4 months ago

History

○

Jon Goss 4 years, 1 month ago

Published this.

○

Jon Goss 5 years, 4 months ago

Gave some feedback: Ready to use

○

Jon Goss 5 years, 5 months ago

Gave some feedback: Needs to be tested

○

Jon Goss 5 years, 5 months ago

Created this.

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

There are 4 other versions that do you not have access to.

Question statement

A coil comprised from {turns} turns is wrapped around a ferrite core carrying a peak flux density of {Bfield} T varying sinusoidally at a frequency of {frequency} kHz. The cross sectional area of the core is {xsection} mm².

Use the values of constant provided in the course when performing calculations. Submit numerical answers to four significant figures and you may use scientific notation.

Give any introductory information the student needs.

			Name	Type	Generated Value

Bfield	number	0.25
flux	number	0.00001025
frequency	integer	20
omega	number	125663.7061435917
turns	integer	280
vmax	number	360.6548366321
xsection	integer	41

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(0.05..0.25#0.05)

JME function reference

Description

Peak B-field amplitude in T.

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`

0.25

→ Used by:

flux

Parts

Flux in the ferrite core Gap-fill
1. Gap Flux Mathematical expression
  Add
Flux value Gap-fill
1. Gap Flux value Number entry
  Add
Time dependence Gap-fill
1. Gap Time dependence Mathematical expression
  Add
Flux linkage Choose one from a list
Maximum voltage Gap-fill
1. Gap Maximum voltage Number entry
  Add

Gap-fill

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

What the mathematical expression for the maximum flux in the ferrite core in terms of one or more of the following variables: $B$ (peak magnetic flux density), $\mu$ (permeability), $A$ (cross-sectional area), $N$ (number of turns) and $f$ (frequency).

$\phi_m=$ Flux

Advice

The point to this question is that we need a time varying field to induce a current. We're told the flux density varies sinusoidally with a given frequency, $f$ , and provided with a peak amplitude, $B_0$ . We're also told that the flux is zero at $t=0$ s. We can therefore express the $B$ -field as

$B(t)=B_0 \sin(\omega t+\gamma)$

where $\omega$ is the angular frequency $2 \pi f$ , and $\gamma$ is the phase angle. Since the flux (and therefore the flux density) is zero at $t=0$ s, the phase angle can be taken to be zero or $\pi$ radians. We can choose zero for simplicity in this case.

The flux is related to the flux density as $\phi(t)=B(t)A$ , and use the relationship that the flux linkage is $\Psi=N\phi$ to write $\Psi(t)$ .

Applying Faraday's Law requires a derivitive of the flux linkage, which is easily obtained as

$\displaystyle{{d\Psi\over dt}={d\over dt}N\phi={d\over dt}NAB(t)=NA{dB(t)\over dt} = N A B_0 \omega \cos(\omega t)}$ .

Hence $|V|=NA\omega B_0=2\pi NAfB_0$ .

Give a worked solution to the whole question.

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
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
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
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet

This question is used in the following exams:

Tutorial sheet 2 - magnetism by Jon Goss in EEE1001 & PHY1023.
All electromag by Jon Goss in EEE1001 & PHY1023.
TEST by Jon Goss in Jon's workspace.
Digital Tutorial: Week 7 by Jon Goss in EEE1001 & PHY1023.

Loading...

Error

Time varying current - Faraday's law

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, 4 months ago

Jon Goss 5 years, 5 months ago

Jon Goss 5 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: `number`

Parts

Gap-fill

Loading...

Error

Time varying current - Faraday's law

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, 4 months ago

Jon Goss 5 years, 5 months ago

Jon Goss 5 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`