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# The Association Of Resistors II

Parallel Association

In a parallel combination of resistors, the voltage across all resistors are equal, and the sum of the currents passing through the resistors is equal to the equivalent resistance of the resistor (the resistor in series, the voltages summed up (V), now which is the sum of the intensity (i)). The equivalent resistance of a parallel combination will always be less than the lowest resistance of the resistor combination.

- Equal voltages: V = V1 = V2 = V3 = V4 [...];
- Current in the equivalent resistor is equal to the sum of the currents of resistors: i = i1 + i2 + i3 + i4 [...];
- The equation that calculates the current at a point of the circuit is: V = i / N, then V / Req = (V1 / R1) + (V2 / R2) + (V3 / R3) + (V4 / R4) [...].

Like all the tensions are equal, we can eliminate them from all terms of the equation:

1 / Req = (1 / R 1) + (1 / R 2) + (1 / R 3) + (1 / R 4) [...].

When working with only two resistors in parallel, we can use the following equation:

Req = (R1. R2) / (R1 + R2).