# What is the Voltage Divider Rule : Examples & Its Applications

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, the output voltage is a fraction of the i/p voltage. The best example for a 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 the frequency response is required over a wide range.

## What is the Voltage Divider Rule?

**Definition:** In the field of electronics, a voltage divider is a basic circuit, used to generate a part of its input voltage like an output. This circuit can be designed with two resistors otherwise any passive components along with a voltage source. The resistors in the circuit can be connected in series whereas a voltage source is connected across these resistors. This circuit is also called a potential divider. The input voltage can be transmitted between the two resistors in the circuit so that the division of voltage takes place.

### When to use the 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. The voltage divider involves 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 different ways that are shown below. But these different circuits should always be the same.

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 the negative terminal. R2 is the resistance between the positive terminal and sliding contact. That means the two resistors R1 and R2 are in series.

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)

Therefore

V (t) =R1i (t)+ R2i (t)= i(t)(R1+R2)

Hence

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

### Resistive Voltage Divider

This is a very easy and simple circuit to design as well as understand. The basic type of a passive voltage divider circuit can be built with two resistors which are connected in series. This circuit uses the voltage divider rule to measure the voltage drop across every series resistor. The resistive voltage divider circuit is shown below.

In the resistive divider circuit, the two resistors like R1 and R2 are connected in series. So the flow of current in these resistors will be the same. Therefore, it provides a voltage drop (I*R) across every resistive.

Using a voltage source, a voltage supply is applied to this circuit. By applying KVL & Ohms Law to this circuit, we can measure the voltage drop across the resistor. So the flow of current in the circuit can be given as

By applying KVL

**VS = VR1 + VR2**

According to Ohm’s Law

**VR1 = I x R1**

**VR2 = I x R2**

**VS = I x R1 + I x R2 = I( R1+R2)**

**I = VS/ R1+R2**

The flow of current through the series circuit is I = V/R according to Ohm’s Law. So the flow of current is the same in both resistors. So now can calculate the voltage drop across the R2 resistor in the circuit

**IR2 = VR2/R2**

**Vs/( R1+R2)**

**VR2 = Vs (R2/ R1+R2)**

Similarly, the voltage drop across the R1 resistor can be calculated as

**IR1 = VR1/R1**

**Vs/( R1+R2)**

**VR1 = Vs (R1/ R1+R2)**

### Capacitive Voltage Dividers

Capacitive voltage divider circuit generates voltage drops across capacitors which are connected in series with an AC supply. Usually, these are used to reduce extremely high voltages for providing a low output voltage signal. Currently, these dividers are applicable in touchscreen-based tablets, mobiles, and display devices.

Not like resistive voltage divider circuits, capacitive voltage dividers works with a sinusoidal AC supply because the voltage division among the capacitors can be calculated with the help of capacitors reactance (X_{C}) that depends on the AC supply’s frequency.

The capacitive reactance formula can be derived as

**Xc = 1/ 2πfc**

Where:

Xc = Capacitive Reactance (Ω)

π = 3.142 (a numeric constant)

ƒ = Frequency measured in Hertz (Hz)

C = Capacitance measured in Farads (F)

Each capacitor’s reactance can be measured by the voltage as well as the frequency of the AC supply & substitute them in the above equation to get the equivalent voltage drops across every capacitor. The capacitive voltage divider circuit is shown below.

By using these capacitors which are connected in the series, we can determine the RMS voltage drop across every capacitor in terms of their reactance once they connected to a voltage source.

**Xc1 = 1/ 2πfc1 & Xc2 = 1/ 2πfc2**

**X _{CT} = X_{C1} + X_{C2}**

**V _{C1} = Vs(X_{C1}/ X_{CT})**

**V _{C2} = Vs(X_{C2}/ X_{CT})**

Capacitive dividers do not allow DC input.

A simple capacitive equation for an AC input is

**Vout = (C1/C1+C2).Vin**

### Inductive Voltage Dividers

Inductive voltage dividers will create voltage drops across coils otherwise inductors are connected in series across an AC supply. It consists of a coil otherwise single winding which is separated into two parts wherever the o/p voltage is received from one of the parts.

The best example of this inductive voltage divider is the auto-transformer including several tapping points with its secondary winding. An inductive voltage divider in between two inductors can be measured through the reactance of the inductor denoted with XL.

The inductive reactance formula can be derived as

XL = 1/ 2πfL

‘XL’ is an inductive reactance measured in Ohms (Ω)

π = 3.142 (a numeric constant)

‘ƒ’ is the frequency measured in Hertz (Hz)

‘L’ is an inductance measured in Henries (H)

The reactance of the two inductors can be calculated once we know the frequency and voltage of the AC supply & utilize them through the voltage divider law to get the voltage drop across every inductor is shown below. The inductive voltage divider circuit is shown below.

By using two inductors that are connected in series in the circuit, we can measure the RMS voltage drops across every capacitor in terms of their reactance once they connected to a voltage source.

**X _{L1} = 2πfL1 & X_{L2} = 2πfL2**

**X _{LT }**=

**X**

_{L1 }+ X_{L2}**V _{L1 }**= Vs (

**X**

_{L1}/ X_{LT})**V _{L2 }**= Vs (

**X**

_{L2}/ X_{LT})AC input can be split by inductive dividers based on inductance:

**Vout = (L2/L1+L2)* Vin**

This equation is for inductors that are non-interacting and mutual inductance in an autotransformer will change the outcomes. The DC input can split based on the resistance of the elements according to the resistive divider rule.

### Voltage Divider Example Problems

The voltage divider example problems can be solved by using the above resistive, capacitive, and inductive circuits.

1). 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 into 4 Ω and 8Ω. The variable resistor is connected across a 2.5 V battery. Let’s examine the voltage that appears across the voltmeter connected across the 4 Ω section of the variable resistor.

According to the voltage divider rule, voltage drops will be,

** Vout= 2.5Vx4 Ohms/12Ohms=0.83V**

2). When the two capacitors C1-8uF & C2-20uF are connected in series in the circuit, the RMS voltage drops can be calculated across every capacitor when they are connected to 80Hz RMS supply & 80 volts.

Xc1 = 1/ 2πfc1

1/2×3.14x80x8x10-6 = 1/4019.2×10-6

=248.8 ohms

Xc2 = 1/ 2πfc2

1/2×3.14x80x20x10-6 = 1/10048 x10-6

= 99.52 ohms

XCT = XC1 + XC2

= 248.8 + 99.52 = 348.32

VC1 = Vs (XC1/ XCT)

80 (248.8/348.32) = 57.142

VC2 = Vs (XC2/ XCT)

80 (99.52/348.32) = 22.85

3). When the two inductors L1-8 mH & L2- 15 mH are connected in series, we can calculate the RMS voltage drop across every capacitor can be calculated once they connected to 40 volts, 100Hz RMS supply.

XL1 = 2πfL1

= 2×3.14x100x8x10-3 = 5.024 ohms

XL2 = 2πfL2

= 2×3.14x100x15x10-3

9.42 ohms

XLT = XL1 + XL2

14.444 ohms

VL1 = Vs (XL1/ XLT)

= 40 (5.024/14.444) = 13.91 volts

VL2 = Vs (XL2/ XLT)

= 40 (9.42/14.444) = 26.08 volts

#### Voltage Tapping Points in a Divider Network

When the number of resistors is connected in series across a voltage source Vs in a circuit, then various voltage tapping points can be considered as A, B, C, D & E

The total resistance in the circuit can be calculated by adding all the resistance values like 8+6+3+2= 19 kilo-ohms. This resistance value will restrict the current flow throughout the circuit which generates the voltage supply (VS).

The different equations which are used to calculate the voltage drop across the resistors are VR1 = VAB,

**VR2 = VBC, VR3 = VCD, and VR4 = VDE.**

The levels of voltage at every tapping point are calculated with respect to GND (0V) terminal. Therefore, the level of voltage at the ‘D’ point will be equivalent to VDE, whereas the level of voltage at the ‘C’ point will be equivalent to VCD + VDE. Here, the level of voltage at point ‘C’ is the amount of the two voltage drops across two resistors R3 & R4.

So by selecting an appropriate set of resistor values, we can make a series of voltage drops. These voltage drops will have a relative voltage value that is attained from only voltage. In the above example, every o/p voltage value is positive as the voltage supply’s negative terminal (VS) is connected to the ground terminal.

#### Applications of Voltage Divider

The **applications of the votlage divider** include the following.

- 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 necessarily to be considered seriously.
- 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 wiping contact that 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 include 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.
- Voltage dividers are used in the measurement of sensor, voltage, shifting of logic level, and adjustment of signal level.
- Generally, the resistor divider rule is mainly used to produce the reference voltages otherwise reducing the voltage magnitude so that measurement is very simple. Additionally; these are works as signal attenuators at low frequency
- It is used in the case of extremely fewer frequencies and DC
- Capacitive voltage divider used in power transmission for compensating load capacitance & high voltage measurement.

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 for you, what is the main function of the voltage divider rule?

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