How Can a Potential Divider Set a Component’s Voltage to Zero?

A potential divider and a series variable resistor are connected differently, so their adjustment ranges work differently. The key is not that one kind of resistor can somehow “stop” current by itself: it is where the component is connected and what voltage appears across it.

How a potential divider controls voltage

A potential divider is commonly made from two resistors connected in series across a supply, or from a potentiometer connected across a supply with its wiper providing the output. Its sliding contact is called the wiper. The output is taken between the wiper and one end of the divider, often the end connected to ground (the supply’s zero-volt reference).

For an unloaded divider with upper resistance $R_1$ and lower resistance $R_2$, the output measured across $R_2$ is

$$V_{\text{out}}=V_s\frac{R_2}{R_1+R_2}.$$

Moving the wiper changes the portions of the potentiometer above and below it. At the grounded endpoint, the lower portion has zero resistance, so the wiper is at ground potential and $V_{\text{out}}=0$. At the other endpoint, the output is approximately the full supply voltage.

If a component is connected from the wiper to ground, it experiences this output voltage. At the grounded endpoint, both of its terminals are connected to the same potential. With zero potential difference across an ordinary resistive component, Ohm’s law gives zero current: $I=V/R=0$.

The divider’s supply current does not necessarily stop. It can still flow through the portion of the divider connected across the supply. The zero-current statement applies to the load connected between the wiper and ground.

Worked example

Suppose a $10\,\text{k}\Omega$ potentiometer is connected across a $12\,\text{V}$ supply. A $1\,\text{k}\Omega$ load is connected from its wiper to ground.

At the midpoint, the potentiometer has about $5\,\text{k}\Omega$ above the wiper and $5\,\text{k}\Omega$ below it. Without a load, the output would be $6\,\text{V}$. The load changes the result because it is in parallel with the lower section:

$$R_{\text{lower,eff}}=5\,\text{k}\Omega\parallel1\,\text{k}\Omega =\frac{5000\cdot1000}{5000+1000}\,\Omega\approx833\,\Omega.$$

Thus the loaded output is approximately

$$V_{\text{out}}=12\frac{833}{5000+833}\approx1.71\,\text{V}.$$

The load draws about $1.71\,\text{mA}$. If the wiper is moved all the way to the grounded end, the output becomes $0\,\text{V}$, so the load current becomes zero in the ideal circuit. In practice, the load can affect the divider’s output at positions away from the endpoint, as this example shows.

Why a series variable resistor behaves differently

A rheostat, or a potentiometer wired as a two-terminal variable resistor, is often placed in series with a load. For a supply $V_s$, load resistance $R_L$, and series resistance $R_V$, the current is

$$I=\frac{V_s}{R_L+R_V}.$$

Increasing $R_V$ makes the current smaller. But for any finite $R_V$, the current remains greater than zero in this ideal model. For example, with a $12\,\text{V}$ supply, a $1\,\text{k}\Omega$ load, and a maximum rheostat setting of $10\,\text{k}\Omega$, the current is

$$I=\frac{12}{11\,\text{k}\Omega}\approx1.09\,\text{mA},$$

not zero. The current would approach zero only as the series resistance became infinitely large. A rheostat can produce zero current if it is adjusted to break the circuit completely, or if a separate switch opens the circuit, but that is different from simply providing a large finite resistance.

The potential divider reaches zero output by setting the load’s voltage to zero at a particular position. A series resistor reduces current by increasing the total resistance in the load’s current path. These are different circuit arrangements, not contradictory behaviors of the same component.

Common mistakes

• Assuming the divider’s current also becomes zero. The divider can still draw current from the supply even when its output is zero.
• Ignoring how the load is connected. Zero output applies when the load is connected between the wiper and the grounded endpoint. A load connected between the wiper and the supply-side endpoint behaves differently.
• Using the unloaded divider formula with a substantial load. The load is in parallel with part of the divider, so it can pull the output away from the unloaded value.
• Treating a finite rheostat setting as an open circuit. A large resistance makes current small, not exactly zero. An open circuit is a separate limiting case.

Practical limits

Real potentiometers have contact resistance, imperfect end connections, and finite tolerances. A circuit may therefore have a tiny residual voltage or current rather than an exact mathematical zero. Also, a divider is best for setting a voltage when the load draws relatively little current; for larger loads, use a suitable buffer or regulator rather than relying on a lightly rated potentiometer.