Potential dividers

A potential divider is a simple circuit that uses two or more resistors in series to split the supply voltage into parts. By choosing suitable resistor values, you can obtain a desired fraction of the total voltage across one of the resistors. This is useful for providing a variable or fixed voltage to another part of a circuit.

Principle of the Potential Divider

When two resistors, $R_1$ and $R_2$, are connected in series across a voltage supply $V_{total}$, the current $I$ is the same through both. The voltage across each resistor is given by Ohm’s law ($V = IR$).

The total resistance is $R_1 + R_2$, so the current is:

$$I = \frac{V_{total}}{R_1 + R_2}$$

The voltage across $R_2$ (the output voltage, $V_{out}$) is:

$$V_{out} = I R_2 = \frac{V_{total} \, R_2}{R_1 + R_2}$$

This formula allows you to calculate the output voltage for any values of $R_1$ and $R_2$.

Potentiometer as a Potential Divider

A potentiometer is a variable resistor with three terminals. It acts as an adjustable potential divider. By moving the slider, you change the resistance ratio and thus the output voltage.

Potentiometers are used to compare potential differences by adjusting the slider until the galvanometer shows zero current (null point). At this point, the potential difference across the known and unknown resistances is equal.

Null Methods and Galvanometers

A null method uses a galvanometer to detect when there is no current flowing through a branch of the circuit. This occurs when the potential difference across the galvanometer is zero. Null methods are highly accurate for comparing voltages because they do not depend on the resistance of the measuring device.

Using Thermistors and LDRs in Potential Dividers

Thermistors and light-dependent resistors (LDRs) are special resistors whose resistance changes with temperature and light intensity, respectively.

• Thermistor: Resistance decreases as temperature increases (usually negative temperature coefficient).
• LDR: Resistance decreases as light intensity increases.

By placing a thermistor or LDR in a potential divider, the output voltage becomes dependent on temperature or light intensity. This is useful in sensors and automatic control circuits.

Summary

• Potential dividers split voltage in proportion to resistor values.
• Potentiometers are variable potential dividers, useful for comparing voltages.
• Null methods with galvanometers provide accurate voltage comparisons.
• Thermistors and LDRs in potential dividers allow the output voltage to depend on temperature or light.