Voltage Division by Series Resistance
Formula Calculation

When a total voltage E_S is applied across series connected resistances R₁ and R₂, the current I_S which flows through the series circuit is:

I_S = E_S / R_S = E_S / (R₁ + R₂)

The voltages V₁ and V₂ which appear across the respective resistances R₁ and R₂ are:

V₁ = I_SR₁ = E_SR₁ / R_S = E_SR₁ / (R₁ + R₂)

V₂ = I_SR₂ = E_SR₂ / R_S = E_SR₂ / (R₁ + R₂)

In general terms, for resistances R₁, R₂, R₃, ... connected in series:

I_S = E_S / R_S = E_S / (R₁ + R₂ + R₃ + ...)

V_n = I_SR_n = E_SR_n / R_S = E_SR_n / (R₁ + R₂ + R₃ + ...)

Note that the highest voltage drop appears across the highest resistance.