Physics (9630) | Potential divider

Voltage Splitting: Understanding the Potential Divider (3.4.5)

Hello! Welcome to the chapter on the Potential Divider. This topic is absolutely central to practical electronics. If you understand circuits, you know that devices often need specific voltages to operate correctly.

Think of your main power supply (like a battery) as a fixed resource—maybe 12 V. What if you need 4 V or 8 V? You can't just plug a 4 V component straight into a 12 V supply without frying it!

That's where the potential divider comes in. You will learn how to use a simple series circuit to split the total voltage into smaller, precise fractions, allowing you to power different components safely and even create clever sensory circuits.

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1. The Function of a Potential Divider

A potential divider is simply a circuit made of two or more resistors connected in series across a power supply. Its purpose is to divide the total potential difference (voltage) supplied into smaller, useful portions.

Key Prerequisite Concepts (A Quick Review)

• Series Circuits: The current (\(I\)) is the same everywhere.
• Kirchhoff's Second Law: The sum of the potential differences (voltages) across all components in a closed loop equals the supply voltage (\(V_{in}\)).
• Ohm's Law: \(V = IR\).

The Voltage Splitting Principle

When resistors are in series, the voltage across each resistor is proportional to its resistance. If one resistor is twice as big as the other, it will take twice the voltage share.

Analogy: The Water Slide of Energy
Imagine the total voltage (\(V_{in}\)) is the height of a water slide. If you build the slide with two sections (representing resistors \(R_1\) and \(R_2\)), the total height drop is split between those sections. If \(R_1\) is bumpy (high resistance) and \(R_2\) is smooth (low resistance), the energy lost (voltage drop) will be greater across the bumpy section.

The output voltage (\(V_{out}\)) is usually taken across only one of the resistors (let's call it \(R_2\)).

2. The Potential Divider Equation

The core skill in this chapter is calculating the voltage across a specific resistor in the chain. We derive the general formula using the basics of series circuits:

Step 1: Calculate the Total Resistance (\(R_T\))

Since the resistors are in series:
\[ R_{T} = R_{1} + R_{2} \]

Step 2: Calculate the Current (\(I\))

Using Ohm's Law for the entire circuit:
\[ I = \frac{V_{in}}{R_{T}} = \frac{V_{in}}{R_{1} + R_{2}} \]

Step 3: Calculate the Output Voltage (\(V_{out}\))

If we define \(V_{out}\) as the voltage across \(R_2\), we use Ohm's Law just for \(R_2\):
\[ V_{out} = I \times R_{2} \]

The Final Potential Divider Formula

Substitute the expression for \(I\) from Step 2 into the equation in Step 3:

The Potential Divider Equation:
\[ V_{out} = V_{in} \left( \frac{R_{2}}{R_{1} + R_{2}} \right) \]

This formula is incredibly important. You must be able to use it, and ideally, understand its derivation.

Key Takeaway: The Potential Divider Equation allows you to calculate the fraction of the input voltage that appears across a specific resistor based on the ratio of that resistor's value to the total resistance.

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3. Applications: Creating Variable Output Voltages

While a fixed potential divider gives a constant fraction of the voltage, the real power comes when one or both of the resistors are variable components. This allows the output voltage (\(V_{out}\)) to change in response to external conditions like light or temperature.

3.1. Variable Resistors (Rheostats)

A variable resistor (often called a rheostat when used this way) can be wired as a potential divider to provide a continuously variable potential difference, often feeding into a device or system that needs adjustable input voltage (like a dimmer switch for a light, although this is a simplified example).

• By sliding the contact point, you change the ratio of resistance above and below the point.
• If the slider is at the bottom, the resistance across \(V_{out}\) is zero, so \(V_{out} = 0\).
• If the slider is at the top, the resistance across \(V_{out}\) is the total resistance, so \(V_{out} = V_{in}\).

The variable resistor setup provides an adjustable output voltage from zero up to the full supply voltage.

3.2. Thermistors (Temperature Sensing)

A thermistor is a resistor whose resistance changes drastically with temperature. In the OxfordAQA syllabus, we focus on Negative Temperature Coefficient (NTC) thermistors.

• NTC Property: As temperature increases, the resistance of the thermistor decreases.

We use a potential divider circuit to convert this resistance change into a usable voltage signal:

Scenario: Using a Potential Divider in a Fridge Alarm
We want an alarm to turn on when the temperature is too high (i.e., the fridge door is left open). We place the thermistor as the resistor \(R_2\), and a fixed resistor \(R_F\) as \(R_1\).

\[ V_{out} = V_{in} \left( \frac{R_{thermistor}}{R_{F} + R_{thermistor}} \right) \]

• If the temperature Rises (Gets warmer): \(R_{thermistor}\) decreases.
• Because \(R_{thermistor}\) is the output resistor, a decrease in its value causes the ratio \(\left( \frac{R_{thermistor}}{R_{F} + R_{thermistor}} \right)\) to decrease.
• Therefore, \(V_{out}\) decreases.

This lowered voltage signal can then be used to trigger a control circuit or alarm when the temperature is too high.

Did you know? Many modern car engines use thermistors in potential divider circuits to monitor coolant temperature and adjust fuel injection rates, ensuring maximum efficiency.

3.3. Light Dependent Resistors (LDRs) (Light Sensing)

A Light Dependent Resistor (LDR) is a component whose resistance depends on the intensity of light falling onto it.

• LDR Property: As light intensity increases, the resistance of the LDR decreases.

Scenario: Automatic Night Light Circuit
We want a light to turn on automatically when it gets dark. We place the LDR as the resistor \(R_2\) (the output voltage resistor), and a fixed resistor \(R_F\) as \(R_1\).

\[ V_{out} = V_{in} \left( \frac{R_{LDR}}{R_{F} + R_{LDR}} \right) \]

• If it gets Darker (Low Light): \(R_{LDR}\) increases dramatically.
• Because \(R_{LDR}\) is the output resistor, an increase in its value means the voltage ratio increases.
• Therefore, \(V_{out}\) increases.

This increased voltage signal (when it gets dark) can be used to switch on a lamp or trigger a street light.

Trick to Remember Sensor Function:
If you want \(V_{out}\) to increase when the condition (light/heat) decreases, place the sensor component in the \(R_2\) (output) position. If you want \(V_{out}\) to increase when the condition increases, place the fixed resistor in the \(R_2\) position and the sensor as \(R_1\)! This reverses the output relationship.

Key Takeaway: Potential dividers are essential for sensor circuits because they translate a non-electrical change (like temperature or light intensity) into a usable electrical signal (voltage change) that can then operate external switches or components.