Question

State the law of combination of resistances in series?

Answer 1

Concept Used:

Step 1: Law of a combination of resistances in series:

The law of combination of resistances in series states that" When a number of resistances are connected in series, their equivalent resistance is equal to the sum of the individual resistances". Thus, if ${\mathrm{R}}_1,{\mathrm{R}}_2,{\mathrm{R}}_3$ are combined in series, then the equivalent resistance $\mathrm{R}$ given by,

$\mathrm{R}={\mathrm{R}}_1+{\mathrm{R}}_2+{\mathrm{R}}_3$

Step 2: Derivation:

We know that, By Ohm's law,

$\mathrm{V}=\mathrm{IR}$

If, $V_1,V_2,V_3$ are the potential difference across the combination of resistances, adding all three potential differences we get,

$\mathrm{V}={\mathrm{V}}_1+{\mathrm{V}}_2+{\mathrm{V}}_3$

$\mathrm{IR}={\mathrm{IR}}_1+{\mathrm{IR}}_2+{\mathrm{IR}}_3$

$\mathrm{IR}=\mathrm{I}({\mathrm{R}}_1+{\mathrm{R}}_2+{\mathrm{R}}_3)$

Canceling on both sides, we get,

$\mathrm{R}={\mathrm{R}}_1+{\mathrm{R}}_2+{\mathrm{R}}_3$

Thus, for a series combination of resistances, the equivalent resistance of the resistances combined in series is equal to the sum of all the resistances.