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 R₁ and R₂ 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 R₁ and R₂. The voltage across the resistor R₁ is V_R1 and the voltage across the resistor R₂ is V_R2.

Thus the voltage drops across the resistors R₁ and R₂ are

$V_{R1} = I R_1 => I = \frac{V_{R1}}{R_1} --->(1)$

$V_{R2} = I R_2 => I = \frac{V_{R2}}{R_2}--->(2)$

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

$V_s = V_{R1} + V_{R2} = I R_1 + I R_2 = I (R_1 + R_2)$

$I = \frac{V_s}{(R_1 + R_2)}--->(3)$

From (1) and (3),

$\frac{V_{R1}}{R_1} = \frac{V_s}{(R_1 + R_2)}$

$V_{R1} = V_s(\frac{R_1}{R_1 + R_2})$

The above equation is the voltage drop across the resistor R₁. Similarly, the voltage drop across the resistor R₂ can be obtained as below.

From (2) and (3),

$\frac{V_{R2}}{R_2} = \frac{V_s}{(R_1 + R_2)}$

$V_{R2} = V_s(\frac{R_2}{R_1 + R_2})$

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

$V_x = V_s(\frac{R_x}{R_T})$

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 R₁ = 20 Ω and R₂ = 40 Ω. The supply voltage across the series resistor is 12V.

Given, R₁ = 20 Ω and R₂ = 40 Ω, V_s = 12 V

R_T = R₁ + R₂ = 20 + 40 = 60 Ω

By applying voltage divider rule, the voltage across the resistor R₁ is

$V_{R1} = V_s(\frac{R_1}{R_1 + R_2}) = 12 (\frac{20}{20 + 40}) = 4 V$