Learning Library · Circuit basics · 3
Kirchhoff's laws and voltage dividers
Two rules account for every volt and every milliamp in a circuit. Voltages around any closed loop add to zero, and currents into any node add to zero. A voltage divider is the simplest place to watch both at work.
Node voltages are labelled in white. Dot speed follows each branch's current on a log scale.
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Kirchhoff's voltage law (KVL)
Walk around any closed loop and add up the voltage rises and drops. They always cancel. In the divider, the source raises the potential by Vin, and R1 and R2 drop it back to zero between them. The table under the schematic does that sum live.
Kirchhoff's current law (KCL)
Charge cannot pile up at a junction, so whatever current flows into a node flows out again. With a load connected, the current through R1 splits at the output node: part goes down through R2 and part through the load.
The voltage divider
That formula only holds when nothing draws current from the output. A load sits in parallel with R2, which lowers the effective bottom resistance and pulls Vout down. Keep the load at least ten times larger than R2 and the error stays under about 5 % for an equal-value divider.
Try this
- Set R1 equal to R2. The output is exactly half the input, and each resistor drops the same voltage.
- Turn on the load and set RL equal to R2. The output falls from one half to one third of Vin.
- Raise RL to 100 times R2. The loaded and unloaded readings now agree to within about 1 %.
- Watch the KCL row while you move any slider. The current into the output node and the currents out of it always balance.
Why your meter matters here
A voltmeter connected to the output is a load too. A typical digital multimeter (DMM) has an input resistance of about 10 MΩ, which is negligible across a 10 kΩ divider but noticeable across a divider built from megohm resistors. When a reading looks low on a high-impedance circuit, the meter itself is a likely cause.
Dividers set reference voltages, scale sensor outputs into an analog-to-digital converter (ADC) range, and bias transistors. They are a poor way to power anything: the output sags as soon as the load current changes.
Check every node yourself. Handheld and bench meters for voltage, current, and resistance.
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