Potential Divider Circuits Explained: A-Level Physics Guide

Introduction to Potential Dividers

In A-Level Physics, understanding how to manipulate voltage is a fundamental skill. A potential divider, often called a voltage divider, is a simple yet powerful circuit configuration used to split a supply voltage into smaller, specific portions. By connecting two or more resistors in series across a power source, you can create a variable or fixed output voltage that is essential for controlling electronic components.

Mastering this topic is vital for your exams, as it forms the basis for sensor circuits. Whether you are designing a system that reacts to light levels or temperature changes, the potential divider is the mechanism that translates physical environmental changes into measurable electrical signals. This guide will walk you through the theory, the mathematics, and the practical applications you need to succeed.

The Principle of the Potential Divider

A potential divider consists of two resistors, $R_1$ and $R_2$, connected in series across a source of electromotive force (e.m.f.), $V_{in}$. Because the components are in series, the same current $I$ flows through both. According to Ohm's Law, the potential difference across each resistor is proportional to its resistance.

The total voltage $V_{in}$ is shared between the resistors such that $V_{in} = V_1 + V_2$. Since $V = IR$, we can derive the output voltage $V_{out}$ across $R_2$ using the ratio of the resistances:

$$V_{out} = V_{in} \times \left( \frac{R_2}{R_1 + R_2} \right)$$

This formula is the cornerstone of potential divider calculations. It shows that the output voltage is a fraction of the input voltage, determined by the ratio of the target resistor to the total resistance of the circuit.

Worked Example 1: Fixed Resistors

Consider a circuit with a $12\text{ V}$ supply connected to two resistors in series: $R_1 = 400\text{ }\Omega$ and $R_2 = 800\text{ }\Omega$. Calculate the output voltage $V_{out}$ across $R_2$.

Step 1: Identify the knowns. $V_{in} = 12\text{ V}$, $R_1 = 400\text{ }\Omega$, $R_2 = 800\text{ }\Omega$.

Step 2: Apply the potential divider formula. $$V_{out} = 12 \times \left( \frac{800}{400 + 800} \right)$$

Step 3: Calculate. $$V_{out} = 12 \times \left( \frac{800}{1200} \right) = 12 \times \frac{2}{3} = 8\text{ V}$$

The output voltage across $R_2$ is $8\text{ V}$.

Using Sensors in Potential Dividers

Potential dividers become truly useful when one of the fixed resistors is replaced with a component whose resistance changes based on external conditions, such as a Light Dependent Resistor (LDR) or a Negative Temperature Coefficient (NTC) thermistor.

• LDRs: As light intensity increases, the resistance of an LDR decreases. If the LDR is $R_1$ in our circuit, increasing light intensity will decrease $R_1$, thereby increasing the fraction of voltage across $R_2$.
• Thermistors: As temperature increases, the resistance of an NTC thermistor decreases. This allows you to create circuits that trigger a response, such as a heater turning on when the temperature drops and the thermistor resistance rises.

Worked Example 2: LDR Sensor Circuit

A potential divider circuit uses a $9\text{ V}$ supply, a fixed resistor $R = 1000\text{ }\Omega$, and an LDR. In bright light, the LDR resistance is $500\text{ }\Omega$. In darkness, it rises to $4000\text{ }\Omega$. Calculate the output voltage across the LDR in both conditions.

Condition 1 (Bright): $$V_{out} = 9 \times \left( \frac{500}{1000 + 500} \right) = 9 \times \left( \frac{500}{1500} \right) = 9 \times 0.333 = 3\text{ V}$$

Condition 2 (Dark): $$V_{out} = 9 \times \left( \frac{4000}{1000 + 4000} \right) = 9 \times \left( \frac{4000}{5000} \right) = 9 \times 0.8 = 7.2\text{ V}$$

Common Mistakes

1. Swapping the Resistors: Students often put the wrong resistance in the numerator of the formula. Remember, the numerator must be the resistance of the component across which you are measuring the output voltage.
2. Ignoring Internal Resistance: In some exam questions, the power supply has internal resistance ($r$). If this is the case, the $V_{in}$ used in the divider formula must be the terminal potential difference, not the e.m.f.
3. Assuming Current is Split: Remember that in a simple series potential divider, the current is the same through both resistors. Do not attempt to split the current as you would in a parallel circuit.

Frequently Asked Questions

What is the main purpose of a potential divider? It is used to provide a specific, reduced voltage from a higher supply voltage, often to control sensors or sensitive components.

How does an NTC thermistor affect the circuit? As temperature increases, the thermistor's resistance decreases, which changes the voltage distribution across the divider.

Can a potential divider be used to power a high-current device? No, potential dividers are generally inefficient for power delivery and are intended for signal control. Connecting a low-resistance load in parallel with one of the resistors will significantly alter the output voltage.

Conclusion

Potential dividers are essential tools for any physicist. By mastering the ratio of resistances, you can design circuits that respond to the world around them. To see these concepts in action with interactive animations, visit MathInstructor AI and generate a free animated lesson on potential divider circuits today.