Parallel

Resistors in parallel share the same voltage but have different currents flowing through them. The total current between the resistors is I_eq=I₁ + I₂.

This is then V/R_eq=V/R₁ + V/R₂.

1/R_eq = I/V= I₁/V₁ + I₂/V₂

1/R_eq= 1/R₁ + 1/R₂

In gereral, the combined resistance of N resistors connected in parallel is 1/R_eq = ∑_i^N(1/R_i). Resistors in a parallel configuration are each subject to the same potential difference (voltage), however the currents through them add. The conductances of the resistors then add to determine the conductance of the network. Thus the equivalent resistance (R_eq) of the network can be computed:

The parallel equivalent resistance can be represented in equations by two vertical lines "||" (as in geometry) as a simplified notation. For the case of two resistors in parallel, this can be calculated using:

As a special case, the resistance of N resistors connected in parallel, each of the same resistance R, is given by R/N.

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