Physics › Electricity › Potential dividers
Potential dividers
Two resistors in series turn one supply voltage into any smaller voltage you like, set purely by a ratio. Swap one resistor for a thermistor or an LDR and the same ratio turns temperature or light into a voltage a circuit can act on.
Builds on Circuits and Kirchhoff's laws.
IN THIS TOPIC
- Explain why series resistors share the supply pd in the ratio of their resistances.
- Calculate a divider's output, and supply a variable pd using a sliding contact.
- Design sensing dividers using thermistors and LDRs, choosing which resistor the output is taken across.
WHAT YOU PROBABLY THINK
The battery decides the voltage across each component.
Sharing in the ratio of the resistances
Put two resistors in series across a supply and the same current threads both, so each takes a pd of V = IR: the shares are proportional to the resistances. The battery fixes only the total; the resistors negotiate the split between themselves. Taking the output across R2 gives
Sanity-check the formula at its limits. Shrink R2 to nothing and the output falls to zero; grow it without bound and the output approaches the full supply. A divider can serve any voltage between the two.
A dial for voltage
Make the split point movable and the divider becomes adjustable. A sliding contact on a resistance track divides it into two parts whose ratio changes as the contact moves, so the output follows the slider, continuously, from zero to the full supply.
This is the volume knob, the dimmer and the joystick axis: one track, one wiper, and a voltage you can dial.
Sensing circuits
Replace one resistor with a component whose resistance responds to the world and the divider becomes a sensor. An ntc thermistor's resistance falls as it warms; a light dependent resistor (LDR) behaves the same way toward light, its resistance falling as the illumination rises. Either way, the changing resistance moves the ratio, and the output voltage tracks the environment.
Design comes down to one decision: which resistor is the output across. With the output across the fixed resistor, warming the thermistor raises the output, the right way round for switching a fan on. Swap the output to the thermistor and the response inverts, which suits a heater instead. The component senses; the position chooses the direction.
THE EXAM BIT
- Read the circuit before the formula: the ratio's numerator is the resistance the output is taken across, over the total. Assuming it is always the bottom resistor is a planted trap.
- Track the share as well as the resistance. When a thermistor warms, its resistance and its share both fall, so the other resistor's share, and any output across it, rises.
- State the LDR's direction explicitly: resistance falls as light intensity rises. Half the marks in an LDR question are for that sentence.
- Check answers against the limits: output between zero and the supply, always. Anything outside that range means the ratio went in upside down.
- For “design a circuit that…” questions, say which component, which position, and which resistor carries the output. All three choices are marked.
CHECK YOURSELF
A divider is built from a 4.0 kΩ resistor above an 8.0 kΩ resistor across a 12 V supply, output across the 8.0 kΩ. (a) Find the output. (b) The 4.0 kΩ resistor is replaced by a thermistor, which then warms up. What happens to the output, and why?
Show a hint
Part (b) needs no numbers: follow the ratio.
Show the answer
(a) Vout = 12 × 8.04.0 + 8.0 = 8.0 V.
(b) Warming an ntc thermistor lowers its resistance, so its share of the 12 V falls, and the share across the fixed 8.0 kΩ resistor, the output, rises toward 12 V. The supply never changed; the ratio did.
Same current, so shares follow resistance.
Change a resistance, move the share.
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