Question

Deduce the expression for the equivalent resistance of three resistors connected in series.

(OR) 

Derive R = R₁ + R₂ + R₃ 

(OR) 

The second end of a first resistor is connected to first end of second resistor. Then how are the resistors connected? Derive the expression for the resultant resistance of this connection.

Answer 1

Series connection: 

In series connection of resistors, there is only one path for the flow of current in the circuit. Hence, the current in the circuit is equal to I. According to Ohm’s law, 

∴ V₁ = IR₁ ; V₂ = IR₂ and V₃ = IR₃. 

Let R be the equivalent resistance of the combination of resistors in series.

Also V = I R_eq 

V = V₁ + V₂ + V₃ 

I R_eq = IR₁ + IR₂ + IR₃ 

⇒ I R_eq = I (R₁ + R₂ + R₃) 

⇒ R_eq = R₁ + R₂ + R₃ 

∴ The sum of individual resistances is equal to their equivalent resistance when the resistors are connected in series.