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Prove. The equivalent resistance R of n resistors R1, R2, ... , Rn 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 Vab. Denote the currents passing through the three resistors R1, R2, and R3 by i1, i2 , and i3. Then, by Ohm’s law
Now the sum of the currents i1, i2 , and i3 going through the resistances must be equal to the line current :
3) i = i1 + i2 + i3
Substituting 2) into 3) gives
equation 5) becomes