Half Divider - Electricity and Electronic Circuits Step by Step

A half-divider scan holds the source fixed and varies matched equal-resistor pairs across three rows, checking that V_out = V_in / 2 stays at half the source even as the current changes 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.

Equal resistors split the source voltage equally. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Equal resistors split equally

The two resistors are both 6 ohm, so the source voltage splits into equal drops.

R_{\text{top}} = R_{\text{bottom}} = 6\ \text{ohm}

Read half the source at the output

Half of 12 volts is 6 volts, so the output node reads 6 volts.

V_{\text{out}} = \frac{12\ \text{V}}{2} = 6\ \text{V}

Equal pairs keep the same half output

The total resistance changes across the rows, so current changes. The output still stays at half the source because the two resistances match.

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