Explore the voltage divider formula, its derivation from Ohm’s law, and its applications in electronics with a practical calculation example.
Understanding the Voltage Divider Formula
A voltage divider is a simple, passive circuit element that splits an input voltage into smaller, proportional output voltages. It is an essential building block in electronics and finds its application in various fields such as power supplies, signal conditioning, and impedance matching. The voltage divider formula is a mathematical expression that helps us calculate the output voltage of a voltage divider circuit.
The Basics of a Voltage Divider Circuit
A voltage divider typically consists of two or more resistors connected in series between a voltage source and ground. The input voltage is applied across the entire resistor network, while the output voltage is taken from a point between two resistors. The current flowing through the resistors is the same, but the voltage drop across each resistor varies according to their resistance values.
Deriving the Voltage Divider Formula
Based on Ohm’s law, we can derive the voltage divider formula. Ohm’s law states that the voltage across a resistor is directly proportional to the current flowing through it and the resistance of the resistor. Mathematically, it can be expressed as:
- VR = I × R
Where VR is the voltage across the resistor, I is the current flowing through the resistor, and R is the resistance.
In a voltage divider circuit, the total current flowing through the resistors (IT) can be calculated using the input voltage (Vin) and the total resistance (RT):
- IT = Vin / RT
The output voltage (Vout) can then be calculated using the current flowing through the resistor connected to the output node (IR) and the resistance of that resistor (RR):
- Vout = IR × RR
As the current through the resistors is the same, we can equate IT and IR and substitute in the expressions above to obtain the voltage divider formula:
- Vout = Vin × (RR / RT)
Using the Voltage Divider Formula
The voltage divider formula allows us to calculate the output voltage of a voltage divider circuit, given the input voltage and the resistors’ values. The formula highlights the importance of choosing appropriate resistor values to achieve the desired output voltage. It is crucial to remember that a voltage divider should not be used to supply power to a load, as it is not designed to provide a stable output under varying load conditions. Instead, voltage dividers are primarily used for signal conditioning and measurement purposes.
Example of Voltage Divider Calculation
Let’s consider a simple voltage divider circuit with two resistors connected in series, R1 and R2. The input voltage, Vin, is 12V. The resistance values of the resistors are R1 = 4kΩ and R2 = 6kΩ. We want to calculate the output voltage, Vout, at the point between the two resistors.
First, we need to determine the total resistance of the circuit, RT:
- RT = R1 + R2 = 4kΩ + 6kΩ = 10kΩ
Now we can apply the voltage divider formula:
- Vout = Vin × (R2 / RT)
Substitute the values into the equation:
- Vout = 12V × (6kΩ / 10kΩ)
Calculate the output voltage:
- Vout = 12V × 0.6 = 7.2V
Thus, the output voltage (Vout) in this example is 7.2V, which is obtained by dividing the input voltage (12V) proportionally according to the resistance values of R1 and R2.
