Question

Question #efb97

Answer 1

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

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`