# Voltage Divider In Series: What, Why, Working, Applications, Detailed Facts

In this article, we shall learn about voltage divider in series. Voltage divider is known to be a linear electrical circuit that provides the output voltage in terms of the input voltage. It is the connection of resistors in series.

A voltage divider is always a series circuit. The simplest voltage divider consists of two resistances in series. Voltage division is essential in creating a variable voltage that helps in voltage measurement, creating complex circuitry. The output voltage obtained by voltage division is a fraction of the input voltage.

## What is voltage divider circuit?

A voltage divider is a simple linear circuit with passive elements. It works on the principle of voltage drop in resistors in series connection. While voltage differs in case of a voltage divider, current remains the same.

A potentiometer is one of the most commonly used  devices that utilizes voltage divider. We can apply a voltage across the terminals of the potentiometer and generate the output voltage. This voltage is proportional to the  position of the sliding contact. By moving this contact, we can change the voltage.

## Voltage divider in series rule?

Voltage divider in series rule gives us an idea about the output voltage in the circuit obtained in terms of input voltage and resistance present in the circuit. Voltage divider in series rule follows ohm’s law.

Voltage drop is the result of current passing through a resistor. This voltage drop is directly proportional to the magnitude of the resistor. According to the rule, voltage across any resistor of the voltage divider is the product of net voltage and a fraction. This fraction is the ratio of that resistance and the equivalent resistance.

## Why use voltage divider in series?

Only a series circuit is capable of voltage division as voltage drops in individual resistors while current passes. In a parallel circuit, the voltage remains the same and current is the quantity that gets divided.

As the name suggests, a voltage divider in series divides the total voltage into two parts which are equal or non equal. If we had to consider the parallel circuit, voltage would have been the same for each branch. In series, there is no branching. The current flows from one resistor to another and drops some value.

## Voltage divider formula for resistors in series

Voltage divider rule says that, the voltage gets divided between two resistive components that are connected in series and these divided voltages are functions of input voltage and the series resistances.

Here, from ohm’s law, we get,

Voltage through R1, [Latex] V_{1}= iR_{1} [/Latex]

Voltage through R2, [Latex] V_{2}= iR_{2} [/Latex]

Applying kirchoff’s law, we can write,

[Latex] -V_{in} + V_{1} + V_{2}= 0 [/Latex]

[Latex] V_{in} = V_{1} + V_{2}= iR_{1} + iR_{2} = i\left ( R_{1}+ R_{2} \right ) [/Latex]

Therefore, [Latex] i = \frac{ V_{in}} {R_{1}+ R_{2}} [/Latex]

Again applying KVL, we can write,

[Latex] V_{out} – iR_{2} = 0 [/Latex]

Or, [Latex] V_{out}= iR_{2} = \frac{ V_{in}} {R_{1}+ R_{2}}\times R_{2} [/Latex]

This is the required divided output voltage.

## Voltage divider rule for capacitors in series

Voltage divider in series rule is just the same as the resistors. Here, the capacitive reactance is analogous to the resistance. The ability of the capacitors to oppose the current flow is known as capacitive reactance.

Capacitive reactance, [Latex] X_{C} = \frac{1} {2\pi fC} [/Latex] where f is the frequency and C is the capacitance.

Therefore, if the net capacitive reactance is XC’ in series then [Latex] X_{C’} = \frac{1} {2\pi fC_{eq}} [/Latex]

Equivalent capacitance in series [Latex] C_{eq} = \frac{C_{1}C_{2}} {C_{1}+C_{2}} [/Latex]

[Latex] X_{C’} = \frac{1} {2\pi f \times \frac{C_{1}C_{2}} {C_{1}+C_{2}}} [/Latex]

So, current [Latex] i= \frac{V_{in}} {X_{C’}} [/Latex]

Now, [Latex] V_{out}= iX_{C_{2}}= \frac{V_{in}} {X_{C’}}\times \frac{1} {2\pi fC_{2}} [/Latex]

## How to calculate voltage in voltage divider?

Voltage dividers are very essential components in amplifiers and controlling circuits. We can calculate voltages in a voltage divider circuit using some simple formulas derived by ohm’s law and kirchhoff’s law.

For calculating the voltage through any resistor, we have to multiply the current with the ratio of that resistance value and equivalent series resistance of the voltage divider. If there’s other elements such as capacitors, the procedure will be the same. Only the resistance will be reactance in that case.

Click to Read more on Voltage vs Voltage Drop: Comparative Analysis.

Kaushikee Banerjee

I am an electronics enthusiast and currently devoted towards the field of Electronics and Communications . My interest lies in exploring the cutting edge technologies. I'm an enthusiastic learner and I tinker around with open-source electronics. LinkedIn ID- https://www.linkedin.com/in/kaushikee-banerjee-538321175