10.3 Potential dividers

For series resistors R₁ and R₂ across supply V_s, the output across R₂ is V_out=V_s R₂/(R₁+R₂).

The output changes when one resistance changes; specify which resistor is measured across and account for loading by a connected device.

With equal resistors across 10 V, the midpoint is 5 V; replacing the lower resistor by a sensor shifts the output.

The output is not always half the supply; that occurs only for equal effective resistances and negligible load.

A potentiometer uses a uniform resistance wire so p.d. is proportional to length; a balance point compares an unknown p.d. with a known reference.

At balance, the detector carries no current, so the comparison is not disturbed by the test source. Keep wire current and uniformity conditions clear.

If a 1.20 V reference balances at 60 cm and an unknown balances at 45 cm on the same wire, the unknown is 0.90 V.

The balance length is not itself a voltage; proportionality requires the same wire current and uniform resistance per unit length.

A galvanometer responds to small current and shows the null condition when its pointer is zero, indicating no potential difference across it.

Use the detector to locate balance rather than to carry substantial circuit current. Reverse connections if needed to identify which side is at higher potential.

Sliding a contact along a potentiometer wire until the galvanometer reads zero identifies the comparison length.

A zero reading does not mean no voltages exist elsewhere; it means the galvanometer’s own terminals have equal potential.

A sensor resistor in a potential divider changes the output voltage when temperature or light intensity changes its resistance.

First state the sensor trend, then identify which resistor the output is measured across; the same resistance change can raise or lower output depending on placement.

An NTC thermistor lowers its resistance when heated; an LDR lowers resistance in brighter light. Both can trigger a voltage threshold in a divider.

The sensor trend alone does not determine output direction—circuit arrangement and loading matter.