Potential Divider Equation (Rearranging)

[rindishy]

Hi.

I'm currently learning about potential dividers and need some help with rearranging the formula.

I've managed to rearrange it to make V_in and R₁ the subject, but I'm having trouble rearranging for R₂.

Can someone help? My maths isn't great, so an explanation would be great. Thanks.

The formula is:

V_out = V_in x R₂/(R₁ + R₂)

 

[Bystander]

What were you wanting from the rearrangement? You've omitted V_out. You can't be trying to eliminate it as a variable.

 

[rindishy]

I want to be able to work out R₂. So if for example I had a question where I was given V_out, V_in and R₁, but not the value of resistance of R₂.

i.e.

R₂ =

 

[Bystander]

Okay. Remember you HAVE to treat both sides of an equation the same way, whatever you do to one side, you do to the other; and you want R₂ in terms of the other three variables. What's a good place to start? How about multiplying both sides by (R₁+R₂) and collecting terms containing R₂ on one side of the equation? Take a stab at it and I'll be right here online for a while --- football games aren't on yet.

 

[HalfLostAndSearching]

Hi there,

Sure, I'd be happy to help you with rearranging the potential divider equation. To start, let's take a look at the original equation:

Vout = Vin x R2/(R1 + R2)

As you mentioned, you have already rearranged it to make Vin and R1 the subject, which gives us:

Vin = Vout x (R1 + R2)/R2

Now, to rearrange for R2, we can start by multiplying both sides of the equation by R2:

Vin x R2 = Vout x (R1 + R2)

Next, we can expand the brackets on the right side of the equation:

Vin x R2 = Vout x R1 + Vout x R2

Now, we can subtract Vout x R2 from both sides of the equation:

Vin x R2 - Vout x R2 = Vout x R1

Factoring out R2 on the left side of the equation, we get:

R2(Vin - Vout) = Vout x R1

Finally, to isolate R2, we divide both sides of the equation by (Vin - Vout):

R2 = Vout x R1/(Vin - Vout)

And there you have it! We have successfully rearranged the potential divider equation to make R2 the subject. I hope this explanation helps and please let me know if you have any further questions. Keep up the good work with your studies!

Best,