And I get the following.

What's drawn right here goes down to here.

And then I try to solve for i2, so once I solve for

i2 I can go back to this expression where I use Vab again.

So this expression is Vab is equal to this part I just brought that down.

And then I made the substitution in here for i 2 and I get this expression.

This right here is the same as this expression right there and

if I simplified it a little bit more I can put it into this form right here.

Now let's look at a couple of special cases.

One is shorted resistors.

So it's equivalent of having a resistance of 0 in parallel with a resistor.

And if I plug that into my formula because I have the product over the sum.

R equals 0 on this side means that the equivalent resistance across here is 0.

And that makes sense because all the current is going

to want to flow right through this way instead of through the other branch.

Because it's lower resistance, it's in fact zero resistance.

Now let's generalize it to K resistors in parallel right here.

It's just one over the sum of their inverses,

however many I have, that's what I have in there.

And for two resistors it simplifies to the product over the sum.

With K resistors, you kind of have to look through this equation right here.