Voltage Divider Formula

A voltage divider is a circuit that is utilized to generate a part of the input voltage as an output. It is typically built using two resistors and a voltage source where the resistors are connected in series. The voltage is then applied across these two resistors. It is also known as a potential divider as it converts a high voltage to a low value. It is a sequence of resistors or capacitors that may be tapped at any point in the circuit to create a precise proportion of the voltage applied between its ends.

Voltage Divider Formula

V_out = V_in × R₂/(R₁ + R₂)

where,

V_out is the output voltage,

V_in is the input voltage,

R₁ is the input resistor,

R₂ is the output resistor.

Derivation of Voltage Divider Formula

Consider the circuit below:

Voltage drop across R1 is V1

Voltage drop across R2 is V2

Input voltage (V) = V1 + V2

According to ohms law,

V1 = I * R1 ⋯⋯⋯➀

V2 = I * R2 ⋯⋯⋯➁

Also,

V = I * R_eq

V = I * (R1 + R2)

⇒I = V/(R1+R2) ⋯⋯⋯➂

substituting ➂ in ➀ and ➁ gives,

V1 = V * R1/(R1 + R2)

V2 = V * R2/(R1 + R2)

Sample Problems on Voltage Divider Formula

Problem 1. Calculate the output voltage of a voltage divider circuit which has two resistors of 3 Ω and 6 Ω and an input voltage of 15 V. The resistor 6 Ω is in parallel to the output voltage.

Solution:

We have,

R₁ = 3

R₂ = 6

V_in = 15

Using the formula we get,

V_out = 15 × (6/(3 + 6))

= 15 × 2/3

= 10 V

Problem 2. Calculate the output voltage of a voltage divider circuit which has two resistors of 2 Ω and 5 Ω and an input voltage of 7 V. The resistor 5 Ω is in parallel to the output voltage.

Solution:

We have,

R₁ = 2

R₂ = 5

V_in = 7

Using the formula we get,

V_out = 7 × (5/(2 + 5))

= 7 × 5/7

= 5 V

Problem 3. Calculate the input voltage of a voltage divider circuit which has two resistors of 3 Ω and 5 Ω and an output voltage of 8 V. The resistor 5 Ω is in parallel to the output voltage.

Solution:

We have,

R₁ = 3

R₂ = 5

V_out = 8

Using the formula we get,

=> 8 = V_in × (5/(3 + 5))

=> 8 = V_in × 5/8

=> V_in = 64/5

=> V_in = 12.8 V

Problem 4. Calculate the input voltage of a voltage divider circuit which has two resistors of 4 Ω and 7 Ω and an output voltage of 49 V. The resistor 7 Ω is in parallel to the output voltage.

Solution:

We have,

R₁ = 4

R₂ = 7

V_out = 49

Using the formula we get,

=> 49 = V_in × (7/(4 + 7))

=> 49 = V_in × 7/11

=> V_in = 539/7

=> V_in = 77 V

Problem 5. Calculate the output resistance of a voltage divider circuit which has an input resistance of 3 Ω, input voltage of 7 V and output voltage of 5 V.

Solution:

We have,

R₁ = 3

V_in = 7

V_out = 5

Using the formula we get,

=> 5 = 7 × (R₂/(3 + R₂))

=> 0.71 + 0.71 R₂ = R₂

=> 0.29 R₂ = 0.71

=> R₂ = 2.44 Ω

Problem 6. Calculate the output resistance of a voltage divider circuit which has an input resistance of 6 Ω, input voltage of 20 V and output voltage of 15 V.

Solution:

We have,

R₁ = 6

V_in = 20

V_out = 15

Using the formula we get,

=> 15 = 20 × (R₂/(6 + R₂))

=> 4.5 + 0.75 R₂ = R₂

=> 0.25 R₂ = 4.5

=> R₂ = 18 Ω

Problem 7. Calculate the input resistance of a voltage divider circuit which has an output resistance of 10 Ω, input voltage of 30 V and output voltage of 20 V.

Solution:

We have,

R₂ = 10

V_in = 30

V_out = 20

Using the formula we get,

=> 20 = 30 × (10/(R₁ + 10))

=> 20 = 300/(R₁ + 10)

=> R₁ + 10 = 15

=> R₁ = 5 Ω