### Using the Calculator

To calculate the **Input Voltage** enter Resistor R1, Resistor R2 and Output Voltage and click Calculate Values.

To calculate the **Output Voltage** enter Input Voltage, Resistor R1 and Resistor R2 and click Calculate Values.

To calculate the value for **Resistor R1** enter Input Voltage, Resistor R2 and Output Voltage and click Calculate Values.

To calculate the value for **Resistor R2** enter Input Voltage, Resistor R1 and Output Voltage and click Calculate Values.

#### What is a voltage divider?

A resistor voltage divider is a simple yet essential circuit used to reduce voltage and create reference voltages. It consists of two resistors connected in series across a voltage supply. The output voltage is taken from the junction of these two resistors. Here’s a detailed explanation of how it works:

#### Basic Principle

The voltage divider works on the principle of voltage drop across resistors in a series circuit. According to Ohm's Law, the voltage drop across a resistor in a series circuit is proportional to its resistance.

#### Voltage Divider Formula

The output voltage \( V_{out} \) is given by the formula:

##### \( V_{out} = V_{in} \times \frac{R2}{R1 + R2} \)

Where:

- \( V_{in} \) is the input voltage.
- \( R1 \) is the resistance of the first resistor.
- \( R2 \) is the resistance of the second resistor.
- \( V_{out} \) is the output voltage.

#### Working Explanation

**Total Resistance**: The total resistance of the series combination is \( R1 + R2 \).**Current Through the Circuit**: Since the resistors are in series, the same current \( I \) flows through both resistors. Using Ohm's Law, the current is:##### \( I = \frac{V_{in}}{R1 + R2} \)

**Voltage Drop Across R1**: The voltage drop across \( R1 \) (let's call it \( V_{R1} \)) is:##### \( V_{R1} = I \times R1 = \frac{V_{in} \times R1}{R1 + R2} \)

**Voltage Drop Across R2**: The voltage drop across \( R2 \) (let's call it \( V_{R2} \)) is:##### \( V_{R2} = I \times R2 = \frac{V_{in} \times R2}{R1 + R2} \)

**Output Voltage**: The output voltage \( V_{out} \) is the voltage across \( R2 \), which is the same as \( V_{R2} \):##### \( V_{out} = \frac{V_{in} \times R2}{R1 + R2} \)

#### Applications

**Reference Voltage Generation**: To provide a specific voltage level lower than the input voltage.**Signal Level Adjustment**: To scale down signal voltages to appropriate levels for further processing.**Biasing Transistors**: To provide necessary biasing voltages in transistor circuits.**Analog-to-Digital Converters (ADC)**: To create specific voltage levels for comparison.

#### Example Calculation

Suppose we have a voltage divider with \( V_{in} = 12V \), \( R1 = 2k\Omega \), and \( R2 = 3k\Omega \).

Using the voltage divider formula:

##### \( V_{out} = 12V \times \frac{3k\Omega}{2k\Omega + 3k\Omega} = 12V \times \frac{3}{5} = 7.2V \)

Thus, the output voltage \( V_{out} \) is 7.2V.