Derive the expression for the equivalent resistance of three resistors connected in Series.

Answer :

1. Two or more resistors are said to be connected in Series, if the amount of current flowing through all the resistors is equal.

2. The total Potential Difference accross the Circuit is equal to the sum of the Potential Differences accross each Resistor.

3. Connect the Circuit as shown in the figure. Let the Current flowing accross the Circuit be 'I', and the Potential Difference accross the circuit be 'V'

4. Let the equivalent resistance provided by the three resistors be R_eq

5. From Ohm's law, we know that R_eq = V/I.

   therefore, V = IR_eq

6. The Potential Differences V₁,V₂,V₃ accross the resistors R₁,R₂,R₃ are given by

   V₁ = IR₁, V₂ = IR₂ and V₃ = IR₃

7. Since the resistors are connected in series,

   V    = V₁ + V₂ + V₃

   IR_eq = IR₁ + IR₂ + IR₃

   I(R_eq) = I(R₁ + R₂ + R₃)

   I(R_eq) = I(R₁ + R₂ + R₃)

   therefore, R_eq = R₁ + R₂ + R₃

   similarly, when n resistors are connected in Series,

   R_eq = R₁ + R₂ + R₃ + ....... + R₁