# Voltage divider | Rule, formula and voltage divider circuit

In the world of electrical and electronics we come across different types of circuits. Those circuits are named differently based on the function which they perform. The components which are used in the circuit are an important part of it. In this article we will learn about a special type of circuit known as voltage divider. This is an electronic circuit which is quite simple and linear in nature. It is the widely used circuit analysis tool. Potential divider circuit is the synonym of voltage divider circuit. In a voltage divider, the output voltage is just a fraction of the input voltage provided. More specifically, the circuit voltage is partitioned or shared or divided among the components of the voltage divider. In this way, the output voltage VOut becomes the function of the input voltage VIn. A typical voltage divider circuit generally consists of an input voltage source and two series connected impedances (or resistances).

An output voltage is obtained across those series connected impedances (or resistances). The output voltage we get is always a fraction of the input voltage of the circuit. Voltage divider is required in those applications, where fraction of the defined input voltage is required for some purpose. There is a voltage divider rule which is applicable for all this divider circuit. Input voltage source may be either dc or ac and voltage divider circuit may be series or parallel in connection. With the help of Ohm’s law we can find out the relation between the input and output voltage of a voltage divider circuit.

## The Voltage Divider Rule

Now we will discuss about the Voltage Divider Rule (VDR). It is the most important rule that governs this kind of circuits. Voltage divider rule says that the voltage measured across particular impedance is equal to the product of the ratio of impedance across which voltage is to be measured to that of the summation of the impedances of the circuit and the input voltage. Let us consider a circuit where two impedances Z1 and Z2, which are connected in series. Voltage Vin is the input voltage of the circuit and Vout is the output voltage, which is measured across the impedance Z2. By applying the voltage divider rule, the Vout = Z2Vin / (Z1 + Z2). And if you consider Vout will be the voltage across Z1, then Vout = Z1Vin / (Z1 + Z2). The voltage divider rule is derived from simple Ohm’s law. Imagine that, you have to determine the voltage across the Z2. The circuit current I is Voltage applied / Total Resistance; that is I = Vin / Z1 + Z2. Now, the voltage across Z2 is simply IZ2. In this way, you can see, whatever be the resistance you consider, the voltage divider rule is equally applicable for any circuit.

Here, the output voltage is just a function of the input voltage, and in other words, the input voltage is divided into the resistance R1 and R2. That is why the circuit is termed as the voltage divider circuit.It will be more easy for you to understand voltage divider rule clearly with the help of an example. Let the impedances are replaced by pure resistances in a series circuit. We will apply voltage divider rule to this circuit. The voltage across the resistance R3 is to be calculated. Input voltage is 15 Volts and resistances R1, R2 and R3 are 5 Ω, 3Ω and 2Ω respectively. Voltage across resistance R3 is given as, Vout = V3 = R3Vin / (R1 + R2 + R3) = 2 X 15 / 5 + 3 + 2 = 2 X 15 / 10 = 3 volts. In this case, the voltage divider rule is applied to determine the voltage across the R3 component. Similarly, the voltage across other two resistances can also be determinded by this simple voltage divider formula.

## Voltage Divider Formula in series and parallel circuits

In a series resistive circuit voltage drop across different resistors can be calculated easily by using the voltage divider rule. At first we have to find out the current through the circuit. As it is a series circuit so obviously the current through each resistor will be the equal. Using simple ohms law I = V / R, value of current is calculated. Here V is the input or source voltage and R is the summation of all resistances in series of the circuit.In this circuit the total resistance is (5+10+15) ohms = 30 ohms and source voltage V is 60 volts. Therefore current through the circuit that is through each resistor is given by, I = V / R = 60 / 30 = 2 Ampere. The voltage across each resistance is calculated from the voltage divider rule as described in the previous example.

• Voltage across R1 5Ω is equal to 5 X 60 / 30 = 10 V
• Voltage across R2 10Ω is equal to 10 X 60 / 30 = 20 V
• Voltage across R3 Ω is equal to 15 X 60 / 30 = 30 V.

Now let us consider the case of a parallel resistive circuit. In parallel circuit voltage across each resistor is the same. Current through different resistors are different in value. Current is determined by the simple ohms law I = V/ R. Current divider rule is best applicable here.

## Types of voltage divider circuits

According to the components of the circuit, there are three different kinds of voltage divider circuit. These are: Resistive voltage divider circuit, Inductive voltage divider circuit and Capacitive voltage divider circuit. We will get a brief idea about each of these types from the following discussion.

Resistive voltage divider: The circuit is purely resistive in nature. That means all components of this circuit are only resistors. Source or supply voltage may be either dc or ac. So by applying the formula of the divider we get the value of the output voltage (ac or dc). In the shown circuit, suppose we have to determine the voltage across the resistance R2. The output voltage across resistor R2 is given as,

Vout = Vin R2 / R1 + R2

So, Vout / Vin = R2 / (R1 + R2 )

Inductive voltage divider: This type of inductor circuit works only on AC voltage input. Input voltage is divided according to the inductance value. Here in the inductances are non interacting in nature as mutual inductance (as in an autotransformer) between two inductors may vary the result of the output voltage. Output voltage is Vout = VinL2 / L1 + L2. If we apply dc supply to this circuit then the voltage will divide according to the resistance of the inductors. This will happen following the resistive voltage divider rule.
Capacitor voltage divider: We all know the property of a capacitor. It can pass AC but always blocks DC. So capacitive voltage divider do not work on dc supply, it performs when there is an ac input voltage. Output voltage in case of capacitive divider can be found out with the help of a formula which is slightly different from those used in resistive or inductive voltage divider circuits. Output voltage is

Vout = VinC1 / C1 + C2.

• Note: There is another special type of voltage divider called the low pass RC filter which consists of a resistor and a capacitor in series. The output voltage is dependent on frequency of the supply voltage and also on RC that is the time constant (τ) of the circuit.

## Applications of voltage divider

Voltage divider circuits are quite useful among the electrical and electronic field. There are many applications of the divider circuits. We will discuss some of them in brief. One of the main applications of the divider is the potentiometer. Working principle of a potentiometer is based upon the voltage divider rule. Potentiometer is a three terminal resistor provided with a siding contact called wiper. Potentiometer finds out voltage (electric potential) with the help of voltage divider formula. As load resistance of the circuit is large with respect to other resistances, so we neglect load resistance and output voltage can be found out using simple resistive voltage divider formula. Since potentiometer is a variable type voltage divider so it finds its applications in gain control, volume controls and other control functions. Other uses of voltage divider circuits are as:

i) AC voltage divider is used as a filter.
ii) Signal level adjustment is another function of the divider.
iii) Network theorem like Thevenin’s theorem uses voltage divider circuit and its rule.
iv) Biasing of active devices in amplifiers.
v) Multi meter and Wheatstone bridge also includes voltage dividers.
vi) Devices like strain gauge and photo resistor uses voltage divider circuits.
vii) Some other practical applications are volume control of radio and television, intensity control of CRT.