What is meant by the voltage division method or voltage divider rule?

In the electronics branch, a voltage divider is required to produce a section of its input voltage as an output. This basic circuit may be prepared with two resistors or any passive elements along with the voltage source. The circuit resistors are attached in series and a voltage source is braced across these resistors. The input voltage can be transferred between the resistors in the circuit for the voltage division to occur. The SI unit of electrical resistance is ohm (Ω) or kilo-ohms (kΩ).

In electrical engineering, the voltage divider rule is one of the most important electronic circuits used for converting a huge voltage into a smaller voltage. Input voltage and two series resistors will give the output voltage which comes out to be a fraction of the input voltage induced. For instance, two resistors connected in series is the best example of a voltage divider circuit. When an input voltage is applied to the two resistors, the output voltage will generate from the connection between them. Dividers are useful for minimizing the magnitude of the voltage or making a reference voltage. Dividers are utilized at low frequencies. For direct current and low frequency, the voltage divider is the ideal method.

The voltage divider rule is used to resolve circuits to simplify the solution. By applying this rule, one may also work out simple circuits thoroughly. The voltage divider includes two important parts; the circuit and the equation. The voltage divider is used only when the voltage is regulated by a voltage drop in a circuit. It is mostly used in systems where energy efficiency is not mandatory to be taken into account. In daily life, it is generally used in potentiometers. Voltage dividers are used to adjust the level of the signal for voltage computation and active devices in amplifiers. A multi-meter and Wheatstone bridge comprise voltage dividers. Voltage dividers are required to measure the resistance of the sensor.

Voltage divider calculation

Consider a circuit having the resistors R₁ and R₂ in series, voltage source connected, and the current flowing through that circuit. Both R₁ and R₂ are connected between the sliding variable and negative or positive terminals respectively. Ohm’s law says V= IR.

Thus, the equations generated are as follows:

V₁ = IR₁ …………… (I)

V₂ = IR₂ …………… (II)

Where,

V₁ = Voltage across resistance R₁

V₂ = Voltage across resistance R₂

I = Current inside the electrical circuit.

Applying Kirchhoff’s Voltage Law which states that the algebraic addition of voltage around a closed path in the circuit is equal to zero,

$V_1 + V_2 = 0$

$V = (R_1 + R_2) I$

$I=\frac{V}{R_1+R_2}$ ……………. (III)

Substitute (III) in (I) and (II) equations, we get

$V_1=R_1\left(\frac{V}{R_1+R_2}\right)$ and $V_2=R_{2 }\left(\frac{V}{R_1+R_2}\right)$ 

Therefore, the voltage divider between the two resistors R₁ and R₂ is directly proportional to the resistance. This voltage divider rule can be applied to circuits that are designed with more than two resistors.

Voltage divider equation

The voltage divider rule equation is used when the three values in the circuit are known, that is, the input voltage and the two resistor values. By using this equation, the output voltage is determined.

$V_{on}=V_i\left(\frac{R_n}{R_1+R_2}\right)$

R₁ and R₂ = Resistors in the circuit

V_on = Output voltage across the resistors R_n, where n=1,2. 

V_i = Input voltage

The above equation depicts that V_o is directly proportional to V_i and the ratio of two resistors R₁ and R₂.

Resistive voltage divider

A passive voltage divider circuit can be created with two resistors that are linked in series. This circuit causes the voltage divider rule to evaluate the voltage drop through each series resistor.

In the resistive divider circuit, the two resistors, R₁ and R₂ are connected in series and thus, the flow of current in these resistors will be the same. So, it provides a voltage drop (IR) across each resistor.

Applying Kirchhoff’s Voltage Law and Ohms Law, the flow of current in the circuit is,

$I=\frac{V_s}{R_1+R_2}$

And the voltage drop across the R₁ resistor is,

$V_1=V_s\left(\frac{R_1}{R_1+R_2}\right)$

Where, V_s = Voltage across resistors R₁ and R₂ connected in series.

V = Total voltage across the circuit.

Capacitive voltage dividers

The capacitive voltage divider circuit produces voltage drops across capacitors which are attached in series with the AC (alternating current) supply. Impedance value must be considered instead of resistance value. These are utilized to minimize very high voltages for giving a low output voltage signal. Applications include touchscreen-based tablets, mobiles, and display devices.

Unlike the resistive voltage divider circuits, the capacitive voltage dividers generate a sinusoidal AC supply as the voltage division among the capacitors can be computed with the assistance of capacitive reactance (X_c) that is dependent on the frequency of the AC supply.

The capacitive reactance equation is,

$X_c=\frac{1}{2\pi fC}$

Where,

X_c = Capacitive Reactance (Ω)

ƒ = Frequency (Hz)

C = Capacitance (F)

Inductive voltage dividers

Inductive voltage dividers generate the voltage drops beyond coils and inductors that are linked in series with the AC supply. Impedance value must be considered instead of resistance value. It comprises a coil or a single winding that is divided into two parts.

For instance, an auto-transformer with many tapping points and a secondary winding. An inductive voltage divider in between the two inductors can be estimated through the reactance of the inductor (X_L).

The inductive reactance formula is,

$X_L=2\pi fL$

X_L = Inductive reactance (Ω)

ƒ = Frequency (Hz)

L = Inductance (H)

Context and Applications

This topic is important for professional exams in both graduate and postgraduate studies and in particular:

• Bachelors in Technology (Electrical Engineering)
• Masters in Technology (Electrical Engineering)
• Masters in Science (Robotics and Electrical Circuits)
• Masters in Science (Machine Learning)

Practice Problems

Q1. What is the SI unit for electrical resistance?

1. Kilogram (kg)
2. Ohm (Ω)
3. Joule (J)
4. Newton (N)

Correct option- b

Explanation: The SI unit for electrical resistance is Ohm (Ω).

Q2.  What produces voltage drops through capacitors that are attached in series with the AC supply voltage?

1. Capacitive voltage divider circuit
2. Voltage divider formula
3. Inductor
4. None of these

Correct option- a

Explanation: The capacitive voltage divider circuit produces voltage drops through capacitors which are attached in series with the AC supply voltage.

Q3. What is the full form of KVL?

1. Kirchhoff’s volume law
2. Kirchhoff’s valve law
3. Kirchhoff’s voltage law
4. None of these

Correct option- c

Explanation: The full form of KVL is Kirchhoff’s voltage law.

Q4. Where is impedance used instead of resistance?

1. Supply voltage ratio
2. Capacitive and inductive voltage dividers
3. Voltage ratio
4. Current ratio

Correct option- b

Explanation: In capacitive and inductive voltage dividers, impedance is used instead of resistance.

Q5. Which of the following statements is incorrect?

1. The input voltage can be transferred between the resistors in the circuit for the voltage division to occur.
2. The purpose of the capacitive voltage divider is in the power transmission for neutralizing load capacitance & high voltage quantification.
3. A passive voltage divider circuit can be created with two resistors are linked in series. This circuit causes the voltage divider rule to evaluate the voltage drop through each series resistor.
4. Capacitive voltage divider circuit produces voltage drops across capacitors which are attached in series with the DC supply voltage.

Correct option- d

Explanation: Capacitive voltage divider circuit produces voltage drops across capacitors which are attached in series with the AC supply.

Related Concepts

• Resistive sensors
• Supply voltage for voltage drop ratios