SolitaryRoad.com

Website owner: James Miller

[ Home ] [ Up ] [ Info ] [ Mail ]

Prove. The equivalent resistance R of n resistors R_{1}, R_{2}, ... , R_{n} connected in parallel is given
by

Proof. We will prove it for three resistors. See Fig. 1.

The potential difference across the terminals of each
resistor must be the same and be equal to V_{ab}. Denote
the currents passing through the three resistors R_{1}, R_{2},
and R_{3} by i_{1}, i_{2} , and i_{3}. Then, by Ohm’s law

Now the sum of the currents i_{1}, i_{2} , and i_{3} going through
the resistances must be equal to the line current :

3) i = i_{1} + i_{2} + i_{3}

Substituting 2) into 3) gives

or

Since

equation 5) becomes

[ Home ] [ Up ] [ Info ] [ Mail ]