Sensor Divider Contrast - Electricity and Electronic Circuits Step by Step

A sensor-divider-contrast scan holds the source and top resistor fixed and varies the bottom (sensor) resistance across three rows, checking that V_out = V_in * R_b / (R_t + R_b) rises as the sensor resistance grows 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.

Changing one resistor changes how the source voltage is divided. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Start with a balanced divider

When the bottom resistance is 3 ohm, the output is 6 volts.

V_{\text{out,low}} = 6\ \text{V}

Increase the bottom resistance

Change only the bottom resistance to 9 ohm.

R_{\text{bottom}} = 9\ \text{ohm}

The output rises

The output changes from 6 volts to 9 volts.

V_{\text{out}}: 6\ \text{V} \rightarrow 9\ \text{V}

More bottom resistance raises the node

With the top resistor fixed, increasing the bottom resistor moves the output node closer to the source voltage. The first and last rows are the two diagrams used above.

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