Voltage Divider with Resistors: Calculation and Application

1️⃣ What is a Voltage Divider?

A voltage divider is a simple circuit used to reduce voltage to a lower value in a predictable ratio. It consists of two or more resistors connected in series, with the output voltage taken from the middle connection.

📌 Key Uses:
✔ Adjust voltage levels for sensors and circuits
✔ Provide reference voltages in electronic devices
✔ Limit input voltage to components

⚠ Not Suitable for Power Supply Conversion!
Voltage dividers should not be used to power devices because they are inefficient and cannot handle high currents.

2️⃣ Basic Voltage Divider Circuit

A voltage divider consists of two resistors (R1 and R2) in series with an input voltage U_in, producing an output voltage U_out (see diagram below).

Circuit Diagram:

   U_in → ─── R1 ───●──── U_out
                    |
                    R2
                    |
                   GND

The output voltage is taken between R1 and R2 and is always lower than U_in.

3️⃣ Voltage Divider Formula

Using Ohm’s Law, the output voltage is calculated as:

$$U_{\text{out}} = U_{\text{in}} \times \frac{R_2}{R_1 + R_2}$$

📌 Key Observations:
✔ If R1 increases, U_out decreases
✔ If R2 increases, U_out increases

This means you can control the output voltage by selecting appropriate resistor values.

4️⃣ How to Calculate Resistor Values

To design a voltage divider, use the formula:

$$R_2 = R_1 \times \frac{U_{\text{out}}}{U_{\text{in}} - U_{\text{out}}}$$

OR

$$R_1 = R_2 \times \frac{U_{\text{in}} - U_{\text{out}}}{U_{\text{out}}}$$

Example Calculation

Given:

• U_in = 12V
• U_out = 5V
• R1 = 10kΩ

Find R2:

$$R_2 = 10kΩ \times \frac{5V}{12V - 5V} = 10kΩ \times \frac{5}{7} = 7.14kΩ$$

In practical circuits, you would choose the nearest standard resistor value (e.g., 6.8kΩ or 7.5kΩ).

5️⃣ Practical Applications of Voltage Dividers

✔ Microcontroller Input Protection – Adjust signal voltage levels
✔ Sensor Voltage Scaling – Convert higher voltages to readable ranges
✔ Reference Voltage Generation – Provide a stable voltage for circuits
✔ Signal Attenuation – Reduce signal strength in analog systems

📌 Example: If a sensor outputs 12V but a microcontroller only accepts 5V, a voltage divider can safely scale the signal.

6️⃣ Important Considerations

🔹 Divider Current (I):
The current through the divider is:

$$I = \frac{U_{\text{in}}}{R_1 + R_2}$$

Too high of a current means wasted power, so choose high-value resistors.

🔹 Load Resistance Effect:
If a device is connected to U_out, its resistance affects calculations. Always ensure R_load >> R2 to avoid incorrect voltage drops.

🔹 Power Dissipation:
Each resistor dissipates power:

$$P = U^2 / R$$

Use resistors with adequate power ratings to prevent overheating.

7️⃣ Summary & Next Steps

✔ Use the voltage divider formula to calculate U_out
✔ Choose R1 and R2 based on required output voltage
✔ Consider power dissipation and load resistance effects

🚀 Next Steps:
✔ Try building a voltage divider on a breadboard
✔ Measure U_out with a multimeter
✔ Experiment with different resistor values

🔌 Voltage dividers are fundamental in electronics and mastering them is crucial for circuit design!