Physics · Ch 11 — Electric Current Through Conductors

Series Combination of Resistors

11.8.2.1

Series Combination of Resistors

In a SERIES combination, resistors are connected one after another along a SINGLE electrical path (Fig. 11.9), so exactly the same current $I$ must flow through every resistor in the chain -- there is nowhere else for the charge to go. Because of this shared current, if two resistors $R_1$ and $R_2$ are in series, the supply voltage divides UNEQUALLY between them (in proportion to their individual resistances): the voltage across $R_1$ is $V_1$ and across $R_2$ is $V_2$ , with the SAME current $I$ through both.

By Ohm's law applied to each resistor separately,

R_1=\frac{V_1}{I},\qquad R_2=\frac{V_2}{I}\qquad\text{--- (11.22)}

and the total supply voltage is the sum of the two individual drops,

V=V_1+V_2\qquad\text{--- (11.23)}

Substituting Eq. (11.22) into Eq. (11.23),

V=I(R_1+R_2)\qquad\text{--- (11.24)}

and writing this as $V=IR_s$ for a single equivalent resistor $R_s$ replacing the pair,

$R_s=R_1+R_2\qquad\text{--- (11.25)}$ …

Figure 11.9Series combination of two resistors R1 and R2

What this figure shows. A single electrical path (loop) circuit diagram showing two resistors R1 and R2 connected end-to-end in a single line (in series), so the same wire (and hence the same current I) passes through both one after the other. The voltage drop across R1 is labelled V1 and the voltage drop across R2 is labelled V2, with the two drops shown as separate segments that together span the full supply voltage V = V1+V2 applied across the …

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