Let us consider two resistances '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 R2 as V2. Since 'V' represents energy, according to the law of conservation of energy V = V1+ V2 ____(1)
Resistors Connected in Series Energized by a Battery
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, 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
