Case1:

Consider two resistances R₁ and R₂ are connected in series across a potential difference of V volts as shown in the figure.

The total current flowing in the circuit is ‘I’ ampere. The voltage drop across R₁ is v₁ and R₂ is v₂ and the total voltage divides into two parts v₁ and v₂.

The equivalent or total resistance is

R_T = R₁ + R₂

Total current I = V/R_eq = V/R₁+R₂

The voltage across resistance R₁,

V₁ =IR₁ = V * R₁/R₁+R₂

Similarly,

V₂= V * R₂/R₁+R₂

Case 2:

In case there are two resistances, similarly for case 2, there are three resistors connected in series and the total resistance will be R_eq= R₁+R₂+R₃

Total current, I = V/R_eq = V/R₁+R₂+R₃

The voltage across resistance R₁,

V₁= IR₁ =V*R₁/R₁+R₂+R₃

Similarly,

V₂= IR₂ =V*R₂/R₁+R₂+R₃

V₃= IR₃ =V*R₃/R₁+R₂+R₃

• Voltage across one of the resistance = Total voltage * same resistance/sum of individual resistance connected in series