Potential dividers
| English | Chinese | Pinyin |
|---|---|---|
| potential divider | 分压器 | fēn yā qì |
| thermistor | 热敏电阻 | rè mǐn diàn zǔ |
| threshold | 阈值 | yù zhí |
| potentiometer | 电位差计 | diàn wèi chà jì |
| null method | 零点法 | líng diǎn fǎ |
| galvanometer | 检流计 | jiǎn liú jì |
The volume knob
- A volume or dimmer knob can set the output anywhere from off to full.
- Inside is a potential divider 分压器 — resistors sharing out the voltage.
- It turns a fixed supply into any voltage you want.
Splitting the voltage
- Two resistors in series share the supply in proportion to their resistance.
- Tapped across $R_2$: $V_{\text{out}} = V_{\text{in}}\dfrac{R_2}{R_1 + R_2}$.
Sharing voltage in series
In a series loop the same current flows everywhere and the cell's voltage splits across the components — that split is how a potential divider works.
A $12\ \text{V}$ supply is across $R_1 = 2.0\ \text{k}\Omega$ and $R_2 = 4.0\ \text{k}\Omega$ in series. What is the output across $R_2$?
$V_{\text{out}} = V_{\text{in}}\dfrac{R_2}{R_1+R_2} = 12 \times \dfrac{4.0}{2.0+4.0} = 8.0\ \text{V}$.
In a potential divider, the p.d. across each resistor is proportional to its resistance.
The same current flows through both, so $V = IR$ means the bigger resistor takes the bigger share.
Sensor circuits
- Swap a resistor for a thermistor 热敏电阻 → the output changes with temperature.
- Swap it for an LDR → the output changes with light.
A thermistor in a divider turns a temperature change into a changing output voltage
Replacing one resistor in a divider with an LDR makes the output voltage depend on:
An LDR's resistance changes with light, so its share of the voltage — the output — tracks the brightness.
Switching at a threshold 阈值
- Feed the changing output to a transistor or comparator.
- It can switch a load on or off when the temperature or light passes a set threshold (e.g. a street lamp at dusk).
A sensor divider can switch a load on when the measured quantity crosses a set ____.
Feed the output to a comparator/transistor; it flips the load when the voltage passes the threshold (e.g. a lamp at dusk).
The potentiometer 电位差计 (null method 零点法)
- A uniform wire taps off $V_x = V_{\text{full}}\dfrac{x}{L_0}$ along its length.
- To compare e.m.f.s, slide until the galvanometer 检流计 reads zero — at balance no current flows, so internal resistance does not matter: $\dfrac{\varepsilon_1}{\varepsilon_2} = \dfrac{l_1}{l_2}$.
Slide the contact until the galvanometer reads zero — at balance the tapped length is proportional to the e.m.f.
At the balance point of a potentiometer, the current through the cell being measured is:
At balance the wire's p.d. exactly opposes the cell's e.m.f., so no current flows through it (a null).
At balance, the measured cell's internal resistance does not affect the result.
With zero current through the cell, there is no $Ir$ drop — so internal resistance has no effect. That is the strength of a null method.
You've got it
- a divider shares voltage by resistance: $V_{\text{out}} = V_{\text{in}}\dfrac{R_2}{R_1 + R_2}$
- a thermistor or LDR makes the output respond to heat or light
- the null method: balance for zero current, so internal resistance has no effect