Potential dividers
The volume knob
- A volume or dimmer knob can set the output anywhere from off to full.
- Inside is a potential divider — 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 $R_2$: $V_{\text{out}} = V_{\text{in}}\dfrac{R_2}{R_1 + R_2}$.
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 → the output changes with temperature.
- Swap it for an LDR → the output changes with light.
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
- 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 (null method)
- 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 reads zero — at balance no current flows, so internal resistance does not matter: $\dfrac{\varepsilon_1}{\varepsilon_2} = \dfrac{l_1}{l_2}$.
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