# Voltage Divider Rule

The voltage divider rule explains, how the voltage gets divided in the circuit when the two or more components are connected in series. The corresponding circuit is called a voltage divider or potential divider circuit.

In this circuit, the voltage is provided to the circuit components from a common voltage supply. Depending on the application, the voltage supply may be 5V, 12V or 24V with respect to the ground point.

## Voltage divider circuit

Consider a series circuit as shown below, which has two resistors R_{1} and R_{2} connected in series. They are connected to the supply source of V_{s} volts.

Let I be the current flowing from the supply. Since it is a series circuit, the same amount of current I flow across the resistors R_{1} and R_{2}. The voltage across the resistor R_{1} is V_{R1} and the voltage across the resistor R_{2} is V_{R2}.

Thus the voltage drops across the resistors R_{1} and R_{2} are

Now by applying the Kirchoff’s Voltage Law(KCL) to the circuit,

From (1) and (3),

The above equation is the voltage drop across the resistor R_{1}. Similarly, the voltage drop across the resistor R_{2} can be obtained as below.

From (2) and (3),

In general, in any series circuit, the voltage across any one of the resistors can be obtained from the formula,

where,

V_{x} – voltage across a particular resistor

V_{s} – total voltage across the series circuit

R_{x} – Value of the particular resistor

R_{T} – Total resistance value of the series circuit.

## Solved Problem 1

**Calculate the voltage drop across each resistor and the current flowing through the circuit consisting of two resistors R _{1} = 20 Ω and R_{2} = 40 Ω. The supply voltage across the series resistor is 12V.**

Given, R_{1} = 20 Ω and R_{2} = 40 Ω, V_{s} = 12 V

R_{T} = R_{1} + R_{2} = 20 + 40 = 60 Ω

By applying voltage divider rule, the voltage across the resistor R_{1} is

Similarly, the voltage across the resistor R_{2} is

The total current can be obtained by using Ohm’s law,

## Solved problem 2

*Calculate the voltage across the three resistors in series in the following diagram.*

The total resistance in the given circuit is given by,

R_{T} = R_{1} + R_{2} + R_{3}= 5 + 10 + 15 = 30 Ω

By applying voltage divider rule in the above given circuit,

The total current in the series circuit is given by,

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