Resistor Divider:
\(V_o = V_i \times \frac{1}{1 + \frac{R_{src}}{R_{load}}}\)
The resistor divider is a common circuit but it is much more valuable as a concept.
The voltage divider represents fundamental circuit behaviour across countless applications.
Battery:
A 9V battery has 100 ohms internal resistance.
What is the output voltage when powering a 900 ohm load?
Power Wiring:
A 100ft long extension cord of 16 AWG copper wire is used with a 1200 W space heater. What is the voltage at the heater?
Appliances are rated assuming nominal voltage (120 V), so a 1200 W heater is really \(R = 120^2/1200 = 12 \Omega\)
16 AWG is 0.004 ohm/ft, so with 100 ft of line and return there is 0.8 ohms.
Therefore the heater will only get:
\(V_o = 120 \times \frac{1}{1 + 0.8/12} = 112.5 V\)