Question

Find the expression for resistors connected in series.

Answer 1

When two or more resistors are joined from end to end, the resistances are connected in series.

The current in series remains the same across all the resistors.

The potential difference is the sum of potential differences across all the individual resistors.

V = V₁ + V₂ + V₃                                                                                       … (1)

Let I be the current in the circuit.

On applying Ohm’s law to the entire circuit, we get

V = IR_s … (2)

Here, R_s is the combined resistance of the circuit.

Now, applying Ohm’s law to individual resistances, we get

V₁ = IR₁

V₂ = IR₂

V₃ = IR₃                                                                                       ......(3)

From equations (1), (2) and (3), we get

IR_s = IR₁ + IR₂ + IR₃

∴ R_s = R₁ + R₂ + R₃

Here, R_s is the resultant resistance. Thus, the resultant resistance of a series combination of resistors is the sum of individual resistances.

The resultant resistance is greater than all the resistances.