Electricity

Let us consider two resistors 'R₁' and 'R₂' connected in series. A battery of 'V' volts is applied to the ends of this series combination. Let us name the potential difference across R₁ as V₁, and that across R₂as V₂. Since 'V' represents energy, according to the law of conservation of energy V = V₁+ V₂ ____(1)

i.e., the total potential difference across the two resistors should be equal to the voltage of the battery.

Using Ohm's law,

V = IR ----------- (1)

V₁ = IR₁ and V₂ = IR₂ ---------- (2)

where I is the current flowing through the circuit and 'R' represents the equivalent resistance of the two resistances.

Substituting (2) in (1)

IR = IR₁ + IR₂

R = R₁+ R₂

Inference

The equivalent resistance is the sum of the individual resistances connected in series. The above result can be generalised for 'n' number of resistances of different values as R = R₁+ R₂ +............ + R_n.