How would you connect two resistors in series? Draw a diagram. Calculate the total equivalent resistance.

Below diagram shows two resistors connected in series:

If current I is drawn from the battery, the current through each resistor will also be I.

By Ohm's law,

p.d. between A and B is V₁ = V_A - V_B = IR₁

p.d. between B and C is V₂ = V_B - V_C = IR₂

Adding these we get,

V = V₁ + V₂

= V_A - V_B + V_B - V_C

= V_A - V_C

= IR₁ + IR₂

= I (R₁ + R₂)    [Equation 1]

If the equivalent resistance between the points A and C is R_S, then the potential difference between the points A and C is

V = V_A - V_C = IR_S    [Equation 2]

Therefore from equation 1 and 2,

IR_S = I (R₁ + R₂)

⇒ R_S = R₁ + R₂

Thus, in the series combination, the equivalent resistance is equal to the sum of the individual resistances.