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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

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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#