Derive the unloaded potential-divider formula.

Solution & explanation

For series R₁ and R₂ across Vin, current I = Vin/(R₁+R₂). Output across R₂ is IR₂, so Vout = VinR₂/(R₁+R₂). A connected load changes the lower branch to its parallel equivalent, so the unloaded formula may no longer give the actual output.