Before learning electrical circuit analysis, we need to familiarize ourselves with the concept of voltage division and current division in an electrical circuit.
This time we will learn the voltage division rule and leave the current divider rule for another time.
A voltage divider is always present in a series circuit while a current divider is always present in a parallel circuit. Since a series circuit has constant current through all circuit elements connected in series, the voltage across each element is determined by their impedance value.
Voltage Division Rule
To make things simpler, assume that we have a simple circuit consisting of a voltage source and several resistors. This circuit can be solved easily with an Ohm’s Law.
The voltage drop across each resistor is proportional to the ohmic value of the resistor.
The current flowing in the circuit is proportional to the total resistance of all the resistors in that circuit.
Using the Ohm’s Law, we can calculate the voltage drop across each resistor as
The voltage across a resistor is equal to the current flowing in the circuit multiplied by the resistance.
Voltage division rule is very popular since voltage divider circuit is widely used for many applications. We can divide a voltage level into a specific percentage of the maximum voltage only by using the correct resistors.
The voltage division rule states that:
The entire voltage supplied across a series connection of numerous resistors is proportionally divided across the resistors.
This shows that the greatest voltage drop will be found across the resistor with the highest resistance. Opposite of that, the smallest voltage drop will be found across the resistor with the lowest resistance.
This voltage division rule is true for both AC circuits and DC circuits.
Keep in mind that we use impedance instead of resistance when dealing with an AC circuit.
Voltage Divider Rule Formula
Our objective here is to be able to calculate the voltage across a specific resistor.
Before understanding why voltage is divided in series circuits, we need to understand the relationship between the voltage, current, and resistance in a series connection.
Observe a simple circuit below with n resistors.
The total resistance in that circuit is
The total current flowing in the circuit is
This is where we use Ohm’s Law to calculate the voltage across a specific resistor. The voltage across resistor R1 will be
The voltage across resistor R2 will be
The voltage across the Rn will be
Now, substituting the total current equation with the voltage across R1 will give us
Substituting the total current equation with the voltage across R2 will give us
Substituting the total current equation with the voltage across Rn will give us
Where:
Vn = voltage drop across the n-th resistor
Rn = resistance of the n-th resistor
The sum of the voltage drop across the n series resistors is equal to the ratio of total current divided by equivalent resistance of the resistors.
We can conclude that:
The voltage drop across an n-th resistor is the product between input voltage and the resistance of the n-th resistor divided by the equivalent series resistance.
This answers the question of why voltage is divided in series circuits. It is because the current in a series circuit is constant through every resistor while the voltage across each resistor depends on its resistance.
Voltage Divider Rule Formula in Series Circuit
Let us do one more calculation and try to understand it fully.
Observe a simple circuit below consisting of a voltage source and three resistors connected in series.
We are now looking for the voltage drop VR1, VR2, and VR3 for each resistor R1, R2, and R3 respectively.
Since the current is equal through each resistor, the voltage drop should only be affected by the resistance value.
How to find individual voltage in a series circuit? Simply by using Ohm’s Law for each resistor will solve this question. The voltage drop are
The total voltage across node X – Y must equal to the sum of the voltage drops across each resistor. As a result we can write:
Substituting each voltage drop with the equation before will give us
The voltage distribution across the individual resistor can be calculated below
How does voltage split in series?
The voltage distribution was estimated using three resistors in series, the method can be used with any number of series connected resistors in a DC circuit or impedance in AC circuit.
Keep in mind that we need to calculate the entire resistance into an equivalent resistance even if we only want to calculate a single voltage drop.
Voltage Divider Circuit
Voltage divider circuit is a circuit to produce the desired voltage level from the voltage source but the current is still the same. The common configuration of a voltage divider circuit is shown below.
Voltage divider circuit only purpose is to divide the voltage source into different voltage levels with respect to the ground.
Since voltage is also known as potential difference, a voltage divider is also known as potential divider.
The voltage source VS applied to the entire series resistors and we can use Kirchhoff’s Voltage Law and Ohm’s Law to calculate the voltage drop across the desired resistor.
The voltage drop across R1 is
The voltage drop across the R2 is
To simplify the equation, the voltage divider equation is
Where Vn is the voltage drop across the n-th resistor, VS is the voltage source, Rn is the resistance of the n-th resistor, and Req is the equivalent series resistance.
Voltage Division Rule Formula Examples
Now let us solve some examples
1. Calculate the voltage drops in the circuit below consists of 2 resistors connected in series
The total resistance or equivalent resistance is
The total current is
The voltage drop across the R1 is
The voltage drop across the R2 is
2. An electrical circuit below consists of 3 resistors with the same resistance. Calculate the voltage drop across each resistor
The equivalent resistance is
The total current is
The voltage drop across each resistor is
3. Below is the common voltage divider circuit only with two resistors. We will get the desired voltage at the VOUT terminal.
Straight to our point, the VOUT will be
Frequently Asked Questions
What is the voltage division rule?
The voltage division rule states that the entire voltage supplied across a series connection of numerous resistors is proportionally divided across the resistors.
How do you know when to use voltage division?
Voltage divider circuit is a circuit to produce the desired voltage level from the voltage source but the current is still the same. The common configuration of a voltage divider circuit is shown below.