# Voltage Divider Rule

The voltage divider rule explains, how the voltage gets divided in the circuit when 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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