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Resistors in parallel

The picture on the left shows a DC voltage source connected with 3 parallel-connected resistors. The question is again: what is the total resistance?

The current in R1 (I1) equals to: I1 = Vbat/R1. And I2 = Vbat/R2, and V3 = Vbat/R3. The total current Itot equals I1 + I2 + I3, so:

Itot = Vbat/R1 + Vbat/R2 + Vbat/R3.

This proves that the total resistance of parallel connected resistors equals to:

1/Rtot = 1/R1 + 1/R2 + 1/R3 + ... or:

In this case, the total resistance is 333Ω. The total current will be 3 ∙ 9mA = 27mA.

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