Proof of Relationship in Parallel Circuit Using Kirchoff's Law

[soul5]

Homework Statement

How do I prove the relationship between the equivalent resistance of a parallel circuit and the values of the constituent resistors exist?

Homework Equations

V=IR

The Attempt at a Solution

Is it because:

I total= I1+I2+I3

and V is the same in parallel so.

V/R total= V/R1 + V/R2 + V/R3

and divide by V so

1/R= 1/R1 + 1/R2 + 1/R3.

is that why?

 

[Dick]

That's exactly why. Well done.