Two resistors in series (Figure 1)

The current (I) flowing through R₁ and R₂ is the same and so the potential differences across them are V₁ = IR₁ and V₂ = IR₂

But using Kirchoff's second rule the total potential difference across them is V = V₁ + V₂ = IR = IR₁ + IR₂ where R is the effective series resistance of the two resistors.

Two resistors in parallel (Figure 2)

The potential difference (V) across each of the two resistors is the same, and the current (I) flowing into junction A is equal to the sum of the currents in the two branches (Kirchoff's first rule) therefore:
I = I₁ + I₂ = V/R = V/R₁ + V/R₂

where R is the effective resistance of the two resistors in parallel.