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# Current Division by Parallel Resistance Formula Calculation

When a total current IP is passed through parallel connected resistances R1 and R2, the voltage VP which appears across the parallel circuit is:

VP = IPRP = IPR1R2 / (R1 + R2)

The currents I1 and I2 which pass through the respective resistances R1 and R2 are:

I1 = VP / R1 = IPRP / R1 = IPR2 / (R1 + R2)

I2 = VP / R2 = IPRP / R2 = IPR1 / (R1 + R2)

In general terms, for resistances R1, R2, R3, ... (with conductance G1, G2, G3, ...) connected in parallel:

VP = IPRP = IP / GP = IP / (G1 + G2 + G3 + ...)

In = VP / Rn = VPGn = IPGn / GP = IPGn / (G1 + G2 + G3 + ...)

where Gn = 1 / Rn

Note that the highest current passes through the highest conductance (with the lowest resistance).

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