How to Do Voltage Division?

To do voltage division, you use a series circuit of resistors to split an input voltage into smaller, proportional output voltages across individual resistors.

What is Voltage Division?

Voltage division is a fundamental concept in electronics used to create a smaller output voltage from a larger input voltage. This is typically achieved by placing two or more resistors in series across the input voltage source. The voltage across each resistor in the series will be a fraction of the total input voltage, proportional to that resistor's resistance compared to the total resistance.

The Voltage Divider Circuit

A basic voltage divider consists of two resistors, R1 and R2, connected in series across an input voltage source, Vin. The output voltage, Vout, is usually taken across one of the resistors, for example, R2.

     Vin
      │
     ┌┴─┐
     │R1│
     └┬─┘
      │
      ├─── Vout (measured across R2)
      │
     ┌┴─┐
     │R2│
     └┬─┘
      │
     GND

For a circuit with multiple resistors R1, R2, ..., Rn in series connected to an input voltage Vin, the voltage across any specific resistor Ri can be determined.

Understanding the Formulas

The principles of voltage division are derived directly from Ohm's Law and the properties of series circuits.

1. Total Resistance: In a series circuit, the total resistance (Rtotal) is the sum of all individual resistances.
   Rtotal = R1 + R2 + ... + Rn (Reference 2)

2. Total Current: According to Ohm's Law (I = V / R), the total current (I) flowing through the series circuit is the total voltage (Vin) divided by the total resistance (Rtotal). Since it's a series circuit, this same current flows through every resistor.
   I = V / R = Vin / Rtotal (Reference 3)

3. Voltage Across a Specific Resistor: The voltage drop (Vi) across any individual resistor (Ri) in the series is given by Ohm's Law (Vi = I * Ri). Substituting the expression for the total current (I) from step 2 gives the voltage division formula.
   Vi = I * Ri
Vi = (Vin / Rtotal) * Ri
Vi = Vin * ( Ri / Rtotal ) (References 1 and 4)

This final formula, Vi = Vin * ( Ri / Rtotal ), is the core of voltage division. It shows that the voltage across a resistor Ri is equal to the total input voltage Vin multiplied by the ratio of Ri to the total resistance Rtotal.

Step-by-Step Voltage Division Calculation

To find the voltage across a specific resistor Ri in a series circuit connected to an input voltage Vin:

1. Calculate the total resistance (Rtotal): Sum the values of all resistors in the series: Rtotal = R1 + R2 + ... + Rn.
2. Identify the resistor of interest (Ri): Determine which resistor you want to find the voltage across.
3. Apply the voltage division formula: Use the formula Vi = Vin * ( Ri / Rtotal ) to calculate the voltage drop across Ri.

Example

Let's say you have a series circuit with two resistors: R1 = 1 kΩ and R2 = 2 kΩ, connected to a 9V input voltage (Vin = 9V). You want to find the voltage across R2 (V2).

1. Calculate Rtotal:
   Rtotal = R1 + R2
Rtotal = 1 kΩ + 2 kΩ = 3 kΩ

2. Identify Ri:
   We want the voltage across R2, so Ri = R2 = 2 kΩ.

3. Apply the formula:
   V2 = Vin * ( R2 / Rtotal )
V2 = 9V * ( 2 kΩ / 3 kΩ )
V2 = 9V * ( 2 / 3 )
V2 = 6V

So, the voltage across the 2 kΩ resistor (R2) is 6V. The remaining voltage (9V - 6V = 3V) would be across R1, which can also be calculated using the formula: V1 = 9V * (1 kΩ / 3 kΩ) = 3V.

Here's a summary in a table:

Key Points

• Voltage division only works with resistors connected in series.
• The output voltage is always less than or equal to the input voltage.
• The voltage across a resistor is directly proportional to its resistance. A larger resistance gets a larger share of the voltage.

Voltage dividers are widely used in circuits, for example, to provide reference voltages, create sensor interfaces (where a sensor's resistance changes with a physical quantity), or scale down voltages for measurement.