Spark image

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.

Resistors in series:  R = R1 + R2

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

Resistors in parallel:  1/R = 1/R1 + 1/R2

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

© Keith Gibbs 2011