A voltage divider is a simple electronic circuit that divides a voltage into smaller fractions using two resistors connected in series. It is a fundamental circuit used in various applications, such as setting reference voltages, biasing transistors, and providing voltage levels to different components.
The basic concept of a voltage divider can be understood through Ohm's Law, which states:
V = I * R
Where:
V is the voltage across a resistor,
I is the current flowing through the resistor, and
R is the resistance of the resistor.
In a voltage divider circuit, we have two resistors in series, connected across a voltage source (usually a higher voltage). The output voltage is taken from the junction between the two resistors. Let's call the resistors R1 and R2. The voltage across each resistor will be proportional to its resistance.
The total voltage across the series combination of R1 and R2 is equal to the supply voltage (V_in), and the current flowing through both resistors is the same (as they are in series).
Using Ohm's Law, we can express the voltage drops across R1 and R2:
V1 = I * R1
V2 = I * R2
Since the current flowing through both resistors is the same, we can equate V1 and V2:
V1 = V2
Now, we can express these voltages in terms of the supply voltage (V_in) and the two resistors (R1 and R2):
V_in = I * R1 + I * R2
Now, since the current (I) is common to both terms, we can factor it out:
V_in = I * (R1 + R2)
Finally, solving for I:
I = V_in / (R1 + R2)
Now that we have the current flowing through the resistors, we can find the voltage drop across each resistor:
V1 = I * R1 = V_in * (R1 / (R1 + R2))
V2 = I * R2 = V_in * (R2 / (R1 + R2))
The voltage across R1 (V1) and the voltage across R2 (V2) represent the fractions of the supply voltage (V_in) that are dropped across each resistor, and these voltages can be considered as the output voltages of the voltage divider.
In summary, a voltage divider works by using two resistors in series to divide the supply voltage into smaller fractions, with the output voltage taken from the junction between the resistors. The voltage across each resistor is proportional to its resistance, and the ratio of the resistances determines the division ratio of the input voltage.