What is the Voltage Divider Rule with Examples?

In electronics, the voltage divider rule is a simple and most important electronic circuit, which is used to change a large voltage into a small voltage. Using just an i/p voltage and two series resistors we can get an o/p voltage. Here, output voltage is a fraction of the i/p voltage.The best example for voltage divider is two resistors are connected in series. When the i/p voltage is applied across the pair of the resistor and the o/p voltage will appear from the connection between them. Generally, these dividers are used to reduce the magnitude of the voltage or to create reference voltage and also used at low frequencies as a signal attenuator. For DC and relatively low frequencies, a voltage divider  may be appropriately perfect if made only of resistors; where frequency response is required over a wide range.

Voltage Divider Rule
Voltage Divider Rule

Voltage Divider Rule

The voltage divider rule is used to solve circuits to simplify the solution.Applying this rule can also solve simple circuits thoroughly The main concept of this voltage divider rule is “ The voltage is divided between two resistors which are connected in series in direct proportion to their resistance. Voltage divider involves of two important parts they are the circuit and the equation.

Different Voltage Divider Schematics

A voltage divider includes a voltage source across a series of two resistors. You may see the different voltage circuits drawn in a different ways that are shown below. But these different circuits should always be the same

Different Voltage Divider Schematics
Different Voltage Divider Schematics

In the above different voltage divider circuits, the R1 resistor is closest to the input voltage Vin, and the resistor R2 is closest to the ground terminal. The voltage drop across resistor R2 is called Vout which is the divided voltage of the circuit

Voltage Divider Calculation

Let us consider the following circuit connected by using two resistors R1 andR2. Where the variable resistor is connected between the voltage source. In the below circuit, R1 is the resistance between the sliding contact of the variable and negative terminal. R2 is the resistance between the positive terminal and sliding contact. That means the two resistors R1 and R2 are in series.

Voltage Divider Rule in Two Series Resistors
Voltage Divider Rule in Two Series Resistors

The ohm’s law states that V=IR
From the above equation, we can get the following equations
V1 (t) =R1i (t)…………… (I)
V2 (t) =R2i (t)…………… (II)


Applying Kirchhoff’s Voltage Law

The KVL states that, when the algebraic sum of voltage around a closed path in a circuit is equal to zero.

-V (t) +v1 (t) +v2 (t) =0
V (t) = V1 (t) +v2 (t)

V (t) =R1i (t)+ R2i (t)= i(t)(R1+R2)
i (t) =v (t) /R1+R2……………. (III)

Substituting III in I and II equations

V1 (t) = R1 (v (t) /R1+R2)
V (t) (R1/R1+R2)
V2 (t) = R2 (v (t) /R1+R2)
V (t) (R2/R1+R2)

The above circuit shows the voltage divided between the two resistors which is directly proportional to their resistance. This voltage divider rule can be extended to circuits which are designed with more than two resistors.

Voltage Divider Rule in More Than Two Series Resistors
Voltage Divider Rule in More Than Two Series Resistors

Voltage division rule for above two resistor circuit
V1(t)= V(t) R1/R1+R2+R3+R4
V2(t)= V(t) R2/R1+R2+R3+R4
V3(t)= V(t) R3/R1+R2+R3+R4
V4(t)= V(t) R4/R1+R2+R3+R4

Voltage Divider Equation

The voltage divider rule equation accepts when you know the three values in the above circuit they are input voltage and the two resistor values. By using the following equation, we can find the output voltage.

Vout=Vin. R2/R1+R2

The above equation states that the Vout (o/p voltage) is directly proportional to the Vin (input voltage) and the ratio of two resistors R1 and R2.

Example of  The Voltage Divider Rule

Let’s assume the total resistance of a variable resistor is 12 Ω. The sliding contact is positioned at a point where resistance is divided in 4 Ω and 8Ω. The variable resistor is connected across a 2.5 V battery. Let’s examine the voltage appears across the voltmeter connected across 4 Ω section of the variable resistor.
According to voltage divider rule, voltage drops will be,

                        Vout= 2.5Vx4 Ohms/12Ohms=0.83V

Applications of Voltage Divider

The voltage divider is used only there where the voltage is regulated by dropping a particular voltage in a circuit. It mainly used in such systems where energy efficiency does not necessary to be considered seriously.

Voltage Divider Rule in Potentiometer
Voltage Divider Rule in Potentiometer

In our daily life, most commonly the voltage divider is used in potentiometers. The best examples for the potentiometers are  the volume tuning knob attached to our music systems and radio transistors, etc. The basic design of the potentiometer includes three pins which are shown above. In that two pins are connected to the resistor which is inside of the potentiometer and the remaining pin is connected with a wipe contact which slides on the resistor. When someone changes the knob on the potentiometer then the voltage will be appeared across the stable contacts and wiping contact according to the voltage divider rule.

Voltage dividers are used to adjust the signal’s level, for voltage measurement and bias of active devices in amplifiers. A multimeter and Wheatstone bridge includes voltage dividers.

Voltage dividers can be used to measure the resistance of the sensor. To form a voltage divider, the sensor is connected in series with a known resistance and known voltage is applied across the divider. The analog to digital converter of the microcontroller is connected to the  center tap of the divider so that tap voltage can be measured. By using the known resistance, measured voltage sensor resistance can be calculated.

This is all about the voltage division rule with circuits, this rule is applicable for both AC & DC voltage sources. Furthermore, any doubts regarding this concept or electronics and electrical projects, please give your feedback by commenting in the comment section below. Here is a question or you, what is the main function of the voltage divider rule?

One Comment

  1. Abraham Joseph says:

    The mention of the practical applications of the voltage divider is very useful.

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