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Resistors in series

Now we'll connect 3 resistors in series with the battery (see picture above). What will be the total resistance of R1, R2 and R3?

The voltage across R1 (V1) equals to: V1 = I∙R1. And V2 = I∙R2, and V3 = I∙R3.

We know that V1 + V2 + V3 = Vbat, so:

Vbat = I∙R1 + I∙R2 + I∙R3 = I∙(R1 + R2 + R3).

This tells us that the total resistance of resistors is series equals to R1 + R2 + R3 + ..., or:

In this case, the total resistance is 3kΩ. The current I will be: 9V / 3k = 3mA.