Question

derive relation between R=R1+R2+R3 when three resistor R1,R2 and R3 are connected in the series in an electric circuit

Answer 1

Consider 3 Resistors with resistance R₁, R₂ & R₃. All there are connected to a cell with voltage of V. Potential Difference across R₁, R₂ & R₃ are V₁, V₂ & V₃ respectively. All these 3 Potential difference make a total of V

V = V₁ + V₂ + V₃

Now the current flowing through the circuit be I.

By Ohm's Law, we know that :

V = I × R

Current will be same through whole circuit. Now let us separate the relation between the each resistors, current flowing and Voltage.

V₁ = I × R₁

V₂ = I × R₂

V₃ = I × R₃

Now using (1) here

V = IR₁ + IR₂ + IR₃

IR = = IR₁ + IR₂ + IR₃

Dividing both sides by I

R = R₁ + R₂ + R₃

The sum of all resistors in a circuit in a series is equal to Total resistance in the series.