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Answer 1 · 2016-10-23T01:17:58

Let the three resistances (resistors) $R_1, R_2 and R_3$ be connected in series as shown in the figure below

![onlinetest.radicesolutions.com]( useruploads.socratic.org )
Let $R_s$ be the resistance of the combination.

We see that as there is only one path for the current to flow. Therefore, the current through each of the resistors is the same.

$I_1=I_2=I_3=I$

By Ohm’s law, the potential differences across the three resistors is,

$V_1 = IR_1, " " V_2 = IR_2, " " V_3 = IR_3$

Also, the voltage drops across the resistors must add up to the total voltage supplied by the battery, we have

$V=V_1+V_2+V_3$
$=>V= IR_1+IR_2+IR_3$
$=>V= I(R_1+R_2+R_3)$ ........(1)

As Ohm's Law must also be satisfied for the complete circuit, we have
$V= IR_s$ ......(2)

Comparing (1) and (2) we have

$R_s=R_1+R_2+R_3$

In general, the equivalent resistance of resistors when connected in series is the sum of all resistances.

$R_("equivalent")=sumR_i$