Parallel resistors formula

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Don Shearman

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From users who are members of MfEP Progress Quizzes :

Hanh Vo

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Ready to use

3 years, 4 months ago

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Don Shearman 10 months, 4 weeks ago

Published this.

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Peter Steele was given access to the Parallel resistors formula 2 years, 11 months ago

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Hanh Vo 3 years, 4 months ago

Gave some feedback: Ready to use

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Don Shearman 3 years, 8 months ago

Created this as a copy of Parallel inductors formula.

Name	Status	Author	Last Modified
Voltage drop formula	Ready to use	Don Shearman	14/05/2024 05:36
Parallel inductors formula	Ready to use	Don Shearman	06/05/2024 05:49
Parallel resistors formula	Ready to use	Don Shearman	06/05/2024 05:53
Heat flow formula	Ready to use	Don Shearman	06/05/2024 05:47

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

Question statement

When two electrical resistors of magnitudes $R_1$ and $R_2$ respectively are connected in parallel the total effective resistance $R$ is given by the formula

$R=\frac{R_1R_2}{R_1+R_2}.$

Give any introductory information the student needs.

			Name	Type	Generated Value

L	integer	90
L1	integer	300
variable	list	[ latex("R_1"), latex("R_2") ]
select	integer	0
sel_var	string	R_1
answers	list	List of 2 items
ans	expression	R*R_2/(R_2 - R)
other_var	string	R_2

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(20..90 #10)

JME function reference

Description

value of R for substitution part of question, random 20 to 90 in steps of 10

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

Can an exam override the value of this variable?

Generated value: `integer`

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Gap 0. Mathematical expression
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2. Gap Gap 1. Number entry
  Add

Gap-fill

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

Rearrange the formula to make $\var{sel_var}$ the subject. (Note: to type a variable such as $R_1$ , type R_1, to enter a fraction such as $\frac{a}{b}$ , type a/b.)

$\var{sel_var}=$ Gap 0. (You must show full working on your ahndwriten working for this part to get full marks)

If $R=\var{L}$ ohms and $\var{other_var}=\var{L1}$ ohms, what is the value of $\var{sel_var}$ ?

$\var{sel_var}=$ Gap 1. ohms (answer to 2 decimal places)

Advice

We have

$\begin{align}R&=\frac{R_1R_2}{R_1+R_2}\quad\text{multiply both sides by }R_1+R_2\\R(R_1+R_2)&=R_1R_2\quad\text{expand the brackets}\\RR_1+RR_2&=R_1R_2\quad\text{subtract }RR_1\text{ from both sides}\\RR_2&=R_1R_2-RR_1\quad\text{factorise RHS}\\RR_2&=R_1(R_2-R)\quad\text{divide both sides by } (R_2-R)\\R_1&=\frac{RR_2}{R_2-R}\end{align}$

$\begin{align}R&=\frac{R_1R_2}{R_1+R_2}\quad\text{multiply both sides by }R_1+R_2\\R(R_1+R_2)&=R_1R_2\quad\text{expand the brackets}\\RR_1+RR_2&=R_1R_2\quad\text{subtract }RR_2\text{ from both sides}\\RR_1&=R_1R_2-RR_2\quad\text{factorise RHS}\\RR_1&=R_2(R_1-R)\quad\text{divide both sides by } (R_1-R)\\R_2&=\frac{RR_1}{R_1-R}\end{align}$

Given $R=\var{L}$ ohms and $\var{other_var}=\var{L1}$ ohms we have

$\begin{align}R_1&=\frac{RR_2}{R_2-R}\\&=\frac{\var{L}\times\var{L1}}{\var{L1}-\var{L}}\\&\approx\var{precround({L}*{L1}/({L1}-{L}),2)}\text{ ohms}\end{align}$

$\begin{align}R_2&=\frac{RR_1}{R_1-R}\\&=\frac{\var{L}\times\var{L1}}{\var{L1}-\var{L}}\\&\approx\var{precround({L}*{L1}/({L1}-{L}),2)}\text{ ohms}\end{align}$

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This question is used in the following exams:

SCC Class Test 1 by Hanh Vo in SCC PrelimMaths.
Don's copy of Class Test 1 for testing by Don Shearman in Don's workspace.
SCC Final Exam by Hanh Vo in SCC PrelimMaths.

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Taxonomy: mathcentre

Taxonomy: Kind of activity

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Checkpoint description

Don Shearman 10 months, 4 weeks ago

Peter Steele was given access to the Parallel resistors formula 2 years, 11 months ago

Hanh Vo 3 years, 4 months ago

Don Shearman 3 years, 8 months ago

Error in variable testing condition

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Generated value: `integer`

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Parallel resistors formula

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Don Shearman 10 months, 4 weeks ago

Peter Steele was given access to the Parallel resistors formula 2 years, 11 months ago

Hanh Vo 3 years, 4 months ago

Don Shearman 3 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`