6.02 The potential divider rule.

The potential divider rule can be used as a quick way of calculating voltage drops, when two resistors in series are connected to an e.m.f.

potential divider

Proof of the potential divider rule.

V₂ = I x R₂ .
I = V_S/R_T .
R_T = R₁ + R₂ .
Therefore I = V_S/(R₁ + R₂) .
Therefore V₂ = V_S/(R₁ + R₂) x R₂ .
rearranging to make the expression look neater gives V₂ = V_S x R₂/(R₁ + R₂) .

Therefore to find the voltage across a resistor in a potential divider circuit, we simply multiply the supply voltage by its resistance divided by the total resistance.

V₂ = V_S x R₂/(R₁ + R₂).

Note the potential divider rule can be used when an e.m.f. is applied to any number of resistors in series.
The voltage across resistor A is given by, V_A = V_S x R_A/R_T .