What is the Voltage Divider Rule?

The Voltage Divider Rule is a fundamental concept in circuit analysis used to determine the voltage across any resistor in a series circuit. In a series circuit, the total voltage ($V_{in}$) is divided among the resistors proportional to their resistance values. The greater the resistance, the larger the voltage drop across it.

The total resistance ($R_{total}$) is simply the sum of all individual resistances: $$\\ R_{total} = R_1 + R_2 + \dots + R_n$$

Once $R_{total}$ is known, the voltage across a specific resistor, $R_x$, is calculated using the general formula: $$V_x = V_{in} \cdot \frac{R_x}{R_{total}}$$

This rule is derived directly from Ohm’s Law ($V=IR$). The current ($I$) is the same throughout the series circuit ($I = V_{in} / R_{total}$). Substituting this into Ohm’s Law for a single resistor ($V_x = I \cdot R_x$) yields the voltage divider formula.

Practical Applications in Electronics

The voltage divider circuit is one of the most common and versatile configurations in electronics. Its utility comes from its ability to scale down a voltage to a desired level.

• Scaling Voltage Levels: It is often used to step down a higher voltage (like a 12V battery) to a lower, usable voltage (like 5V or 3.3V) required by microcontrollers or sensors.
• Sensor Interfaces: Many analog sensors (like light-dependent resistors or thermistors) are naturally integrated into voltage dividers. As the sensor’s resistance changes with an environmental factor (light, temperature), the output voltage ($V_{out}$) of the divider changes proportionally, allowing the signal to be read by an Analog-to-Digital Converter (ADC).
• Biasing Circuits: Voltage dividers are used to set the operating point (bias) of transistors, ensuring they operate reliably in the desired active region.
• Potentiometers: A potentiometer is essentially a variable voltage divider, allowing a user to continuously select a desired fraction of the input voltage.

How to Use This Tool

1. Input Total Voltage: Enter the value for $V_{in}$ (the source voltage) in the first box. This is typically the battery or power supply voltage.
2. Set Resistor Count: Enter the total number of resistors ($N$) in series (must be 2 or more). The resistor input fields will automatically adjust.
3. Enter Resistance Values: Input the resistance value (in Ohms, $\Omega$) for each resistor ($R_1, R_2, \dots, R_n$).
4. Calculate: Click the “Calculate Voltages” button.
5. View Results: The “Calculation Results” section will display the total equivalent resistance ($R_{total}$), the total current ($I$), and the individual voltage drop ($V_x$) across each resistor, correctly formatted with LaTeX.