Divider Node Voltage - Electricity and Electronic Circuits Step by Step

A divider-node-voltage scan holds the source fixed and varies the top and bottom resistors across three rows, checking that the output V_out = V_in * R_b / (R_t + R_b) takes the bottom share of the total resistance row by row. The arithmetic is exact only for the stated source voltages, resistances, currents, output voltages, and rows in the ideal resistor, ideal supply, high-impedance measurement model. Real dividers add resistor tolerance, source resistance, load impedance, temperature drift, meter/probe calibration limits, finite precision, and measurement uncertainty.

A voltage divider uses two resistor drops to make a node voltage. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A divider is two resistors in series

The output node sits between the top resistor and the bottom resistor.

\text{output node is between the two drops}

Compute the series current

The source is 12 volts. The resistors are 2 ohm and 4 ohm, so the current is 2 amperes.

I = \frac{12\ \text{V}}{2\ \text{ohm} + 4\ \text{ohm}} = 2\ \text{A}

Compute the two drops

The top resistor drops 4 volts. The bottom resistor drops 8 volts, and that bottom drop is the output voltage.

V_{\text{out}} = V_{\text{bottom}} = 8\ \text{V}

The output is the bottom share

Keep the source at 12 volts. The output follows the fraction of total resistance below the output node. The diagram shows the middle row.

\begin{array}{c|c|c|c|c|c}V_{\text{in}}&R_t&R_b&I&V_t&V_{\text{out}}\\12\ \text{V}&1\ \text{ohm}&3\ \text{ohm}&3\ \text{A}&3\ \text{V}&9\ \text{V}\\12\ \text{V}&2\ \text{ohm}&4\ \text{ohm}&2\ \text{A}&4\ \text{V}&8\ \text{V}\\12\ \text{V}&3\ \text{ohm}&3\ \text{ohm}&2\ \text{A}&6\ \text{V}&6\ \text{V}\\\end{array}