Resistors in Series

physicselectromagnetism/circuitsdifficulty 1/5#ohm#series#resistance

A battery of EMF $V$ drives a current through two resistors $R_1$ and $R_2$ connected in
series. Find the equivalent resistance $R_{eq}$ of the pair.

VV R1R1 R2R2
Two resistors in series across a battery of EMF $V$.
Answer & solution

Answer

$ R_{eq} = R_1 + R_2 $

Solution

The same current $I$ flows through both resistors, and the potential drops add:
$V = IR_1 + IR_2 = I(R_1 + R_2)$. Comparing with $V = I R_{eq}$ gives
$$R_{eq} = R_1 + R_2.$$