I have a problem

Kets · #1 $Old$ September 7th, 2008, 11:19 AM

Ok, my sister needs to do this problem where you get r_2 on one side and everything else on the other.
This is what I have so far:

(1/R) = (1/r_1)+(1/r_2)
(1/R) - (1/r_1) = 1/r_2
r_2((1/R) - (1/r_1)) = 1
r_2 = 1/((1/R) - (1/r_1))

What do i do next?

Chris L T521 · #2 $Old$ September 7th, 2008, 11:27 AM

Quote:

Originally Posted by Kets $View Post$

Ok, my sister needs to do this problem where you get r_2 on one side and everything else on the other.
This is what I have so far:

(1/R) = (1/r_1)+(1/r_2)
(1/R) - (1/r_1) = 1/r_2
r_2((1/R) - (1/r_1)) = 1
r_2 = 1/((1/R) - (1/r_1))

What do i do next?

What you found for $r_2$ is correct, but I'd suggest that you should simplify the right side:

$r_2=\frac{1}{\displaystyle\frac{1}{R}-\frac{1}{r_1}}$

First multiply both the numerator and the denominator of the fraction by $Rr_1$ (the common denominator of $\frac{1}{R}$ and $\frac{1}{r_1}$ )

$r_2=\frac{1}{\left(\displaystyle\frac{1}{R}-\frac{1}{r_1}\right)}\cdot\color{red}\frac{Rr_1}{Rr_1}$

This will yield the result:

$r_2=\frac{Rr_1}{\displaystyle\frac{Rr_1}{R}-\frac{Rr_1}{r_1}}\implies\color{red}\boxed{r_2=\frac{Rr_1}{r_1-R}}$

I hope this makes sense!

--Chris

Kets · #3 $Old$ September 7th, 2008, 11:37 AM

Thank you!