Describe the action of a variable potential divider

4.3.3 Action and Use of Circuit Components

Objective

Describe the action of a variable potential divider.

What is a \cdot ariable Potential Divider?

A variable potential divider is a resistive device that provides an adjustable output voltage from a fixed supply voltage. By changing the resistance ratio, the fraction of the supply voltage appearing across a portion of the device can be varied continuously.

Basic Principle

The device consists of a uniform resistive track with a movable contact (wiper). The total resistance of the track is \$R_{\text{total}}\$. When the wiper is at a distance \$x\$ from one end, the resistances on either side are:

\$\$

R1 = R{\text{total}} \frac{x}{L}, \qquad

R2 = R{\text{total}} \left(1-\frac{x}{L}\right)

\$\$

where \$L\$ is the total length of the resistive track.

The output voltage \$V_{\text{out}}\$ taken between the wiper and the nearer end is given by the potential divider formula:

\$\$

V{\text{out}} = V{\text{s}} \frac{R2}{R1 + R2} = V{\text{s}} \frac{R2}{R{\text{total}}}

\$\$

or, using the position ratio,

\$\$

V{\text{out}} = V{\text{s}} \left(1-\frac{x}{L}\right)

\$\$

Thus moving the wiper changes \$V_{\text{out}}\$ proportionally.

Types of \cdot ariable Potential Dividers

• Potentiometer – a three‑terminal device used to obtain a variable voltage while the wiper draws negligible current.
• Rheostat – a two‑terminal device (one end and the wiper) used to vary resistance in a circuit, often for controlling current.

Key Characteristics

How to Use a \cdot ariable Potential Divider in a Circuit

1. Connect the two fixed ends of the resistive track across a stable supply voltage \$V_{\text{s}}\$.
2. Connect the load (or measuring instrument) between the wiper and the appropriate fixed end.
3. Adjust the wiper position until the desired output voltage \$V_{\text{out}}\$ is obtained.
4. For accurate voltage division, ensure the load resistance \$R_{\text{L}}\$ is much larger than the resistance of the portion of the track it is connected to, so that the voltage division is not significantly altered.

Practical Considerations

• Load effect: If \$R{\text{L}}\$ is comparable to \$R2\$, the effective division changes. The modified output voltage is \$V{\text{out}} = V{\text{s}} \frac{R2 \parallel R{\text{L}}}{R1 + (R2 \parallel R_{\text{L}})}.\$
• Power rating: The resistive track must be able to dissipate the power \$P = I^2 R\$ without overheating.
• Linearity: Uniform resistivity of the track gives a linear relationship between wiper position and voltage.
• Mechanical wear: Repeated movement can wear the contact, affecting reliability.

Example Calculation

Given a 10 kΩ potentiometer connected across a 12 V supply. The wiper is positioned at 30 % of the total length from the left end. Find the voltage between the wiper and the left end.

Solution:

\$\$

x = 0.30 L \quad\Rightarrow\quad V{\text{out}} = V{\text{s}} \left(1-\frac{x}{L}\right) = 12\ \text{V} \times (1-0.30) = 12\ \text{V} \times 0.70 = 8.4\ \text{V}

\$\$

The output voltage is 8.4 V.

Common Applications in IGCSE Experiments

• Adjusting the brightness of a lamp in a circuit.
• Calibrating a voltmeter using a known voltage source.
• Providing a variable reference voltage for transistor biasing.

Summary

A variable potential divider allows a fixed supply voltage to be split into a controllable output voltage by varying the ratio of two resistances within a single component. Understanding the relationship \$V{\text{out}} = V{\text{s}} \frac{R2}{R1+R_2}\$ and the effect of load resistance is essential for accurate use in circuits.