Voltage Divider
Vout, loading current, and dissipation for the two-resistor divider.
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The engineering
The most-built circuit in electronics. The Thévenin resistance row is the part people forget: it is the source impedance your ADC or scope input sees, and with a 10 MΩ meter it is why high-value dividers read low.
Keep divider current ~10× the load current for a stiff reference, and check the mW rows against package ratings before you smell why.
Where this math comes from
The divider is Ohm's law applied twice, but its formal footing is Gustav Kirchhoff, who published his circuit laws in 1845 while still a 21-year-old student — the voltage and current laws that make series-parallel analysis routine.
Léon Charles Thévenin, an engineer at the French telegraph administration, showed in 1883 that any such network collapses to one source and one resistance — the row at the bottom of this card, and the reason dividers and real instruments don't always agree.
- 1827Georg Simon OhmV = IR — the law the divider applies twice.
- 1845Gustav KirchhoffCircuit laws, published at age 21, formalize series-parallel analysis.
- 1883Léon Charles ThéveninEquivalent-circuit theorem — the divider's output impedance.
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