PHYS345 Electricity and Electronics

Parallel Circuits

Three resistors in parallel
  Equivalent simple circuit
The voltage difference is the same across each resistor; in essence that is the definition of "parallel."

V = V1 = V2 = V3

The current through the battery is shared by the three resistors. How the current splits among the three branches is determined by the relative resistance of each resistor.

i = i1 + i2 + i3

Combining the two equations via Ohm's law:

i = V1/R1 + V2/R2 + V3/R3

  The simple equivalent circuit is required to have the same current through the battery, given the same applied voltage:
i = V (1/R1 + 1/R2 + 1/R3)
i = V /Req

Comparison of the equations above yields:

1/Req = 1/R1 + 1/R2 + 1/R3

Resistors in parallel

Last updated Sept. 2, 1998.
Copyright George Watson, Univ. of Delaware, 1998.