Resistance

With two ideal resistors, how do you work out their resistance if you know what they equal in parallel and series?

Question:
In series, the total resistance is 30 ohms
In parallel, the total resistance is 7.2 ohms

Work out the value of each resistor and how you would calculate the values.

Reply 1

Stonebridge

13

Original post by rm2

With two ideal resistors, how do you work out their resistance if you know what they equal in parallel and series?

Question:
In series, the total resistance is 30 ohms
In parallel, the total resistance is 7.2 ohms

Work out the value of each resistor and how you would calculate the values.

Welcome to TSR Physics.

2 Simultaneous equations.
One for the sum in series and the other for the parallel combination.
You'll get a quadratic equation to solve at the end.

Reply 2

rm2

OP

Original post by Stonebridge

Welcome to TSR Physics.

2 Simultaneous equations.
One for the sum in series and the other for the parallel combination.
You'll get a quadratic equation to solve at the end.

Thanks, could you possibly go a bit more in depth because I'm still confused.

I know that R1 + R2 = 30

And R1xR2 ÷ R1+R2 = 7.2

So I put them both together to get R1xR2 ÷ 30 = 7.2

And then got R1xR2 = 216 but I don't know where to go from here.

Reply 3

lerjj

13

Original post by rm2

Thanks, could you possibly go a bit more in depth because I'm still confused.

I know that R1 + R2 = 30

And R1xR2 ÷ R1+R2 = 7.2

So I put them both together to get R1xR2 ÷ 30 = 7.2

And then got R1xR2 = 216 but I don't know where to go from here.

Unless I'm missing something, that's not the equation for adding resistors in parallel.

Spoiler

Reply 4

rm2

OP

Original post by lerjj

Unless I'm missing something, that's not the equation for adding resistors in parallel.

Spoiler

Thats the correct equation for parallel resistance AFAIK. 7.2 is 36 ÷ 5

Reply 5

lerjj

13

Original post by rm2

Thats the correct equation for parallel resistance AFAIK. 7.2 is 36 ÷ 5

Right, got it. Never seen it in that format before for some reason. I've always seen it as\dfrac{1}{R_t}=\dfrac{1}{R_1}+ \dfrac {1}{R_2}

You solve simultaneous equations by rearranging one eq for one variable and then substituting this into the other.

So R1=30-R2, substitute this into another equation to eliminate R1, solve for R2 and then substitute that back into an equation.

Reply 6

Stonebridge

13

Original post by rm2

Thanks, could you possibly go a bit more in depth because I'm still confused.

I know that R1 + R2 = 30

And R1xR2 ÷ R1+R2 = 7.2

So I put them both together to get R1xR2 ÷ 30 = 7.2

And then got R1xR2 = 216 but I don't know where to go from here.

Yes and R₁ + R₂ = 30

Sub an expression for R₁ or R₂ from one equation into the other.
You will get a quadratic.

Reply 7

rm2

OP

Okay thanks guys, I'll try doing that tommorow (really tired xd) and get back if I still need help.

Reply 8

rm2

OP

Turns out I still can't complete the question. I've rearranged to find that R1 = 216 ÷ R2 and R2 = 216 ÷ R1
But I dont know what to do after that. I tried substituting the values into another equation but I end up cancelling them out and get something like 216 = 216 lol

Reply 9

Stonebridge

13

You have, so you say,
R₁R₂ = 216
and
R₁ + R₂ = 30

Assuming these are correct, then
Sub R₁ = 30 - R₂
for the R₁ in
R₁R₂ = 216
You then have an equation with just R₂ unknown.
It's a quadratic.

Resistance

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