4.3.3 Action and use of circuit components
- Syllabus
- 0625–2026–2027
- Topic
- 4.3.3
- Level
- —
Learning objectives
4.3.3.1P.d. across an electrical conductor• Know: the p.d. across an electrical conductor increases as its resistance increases for a constant current4.3.3.2Action of a variable potential divider• Describe the action of a variable potential divider4.3.3.3Potential divider relation: R1/R2 =• Recall/use potential divider relation: R1/R2 = V1/V2
Relate p.d. to resistance at constant current
For a conductor carrying a constant current, the potential difference across it increases when its resistance increases. This follows directly from V=IR.
V=IR\qquad\text{and, when }I\text{ is constant, }V\propto R
The same 0.40 A flows through a 10 Ω conductor and a 20 Ω conductor in series. Their p.d.s are 0.40imes10=4.0 V and 0.40imes20=8.0 V, so the conductor with twice the resistance has twice the p.d.
The conclusion requires the current to be constant. If both resistance and current change, compare them with V=IR rather than assuming that p.d. must follow resistance alone.
Control an output with a potential divider
A potential divider has two resistive sections in series across a supply, with the output taken across one section. The fixed supply p.d. is shared: the section with the larger resistance has the larger share.
| Divider action | What changes | Effect on output |
|---|---|---|
| sliding contact on one resistor | the resistance above and below the slider | the output can move continuously from about 0 V to the full supply p.d. |
| LDR plus fixed resistor | LDR resistance falls as light intensity rises | p.d. across the LDR falls; p.d. across the fixed resistor rises |
| NTC thermistor plus fixed resistor | thermistor resistance falls as temperature rises | p.d. across the thermistor falls; p.d. across the fixed resistor rises |
To predict a change: identify the component across which Vout is measured, decide how that component's resistance changes, then compare its share of the total series resistance. Moving a slider towards one end shortens one resistive section while lengthening the other, so the two output shares change in opposite directions.
The output is measured between the slider or junction and one supply terminal. Reversing which section the output is taken across reverses whether the output rises or falls.
Calculate a potential-divider output
Two series resistors carry the same current, so their potential differences are in the same ratio as their resistances.
\frac{R_1}{R_2}=\frac{V_1}{V_2}
V_1=V_{\text{supply}}\frac{R_1}{R_1+R_2}\qquad V_2=V_{\text{supply}}\frac{R_2}{R_1+R_2}
A 1.2 kΩ resistor and a 2.4 kΩ thermistor are in series across 6.0 V, with the output across the thermistor. Vout=6.0imes2.4/(1.2+2.4)=4.0 V. Check: the thermistor is two-thirds of the total resistance and receives two-thirds of the supply p.d.
Use the resistance of the same section that the output is measured across in the numerator. The two p.d.s must add to the supply p.d.; the ratio formula assumes the two components are in series and carry the same current.