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
Vout = Vin × R2/(R1 + R2)
where,
Vout is the output voltage,
Vin 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 * Req
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
Vin = 15
Using the formula we get,
Vout = 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
Vin = 7
Using the formula we get,
Vout = 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
Vout = 8
Using the formula we get,
=> 8 = Vin × (5/(3 + 5))
=> 8 = Vin × 5/8
=> Vin = 64/5
=> Vin = 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
Vout = 49
Using the formula we get,
=> 49 = Vin × (7/(4 + 7))
=> 49 = Vin × 7/11
=> Vin = 539/7
=> Vin = 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
Vin = 7
Vout = 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
Vin = 20
Vout = 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
Vin = 30
Vout = 20
Using the formula we get,
=> 20 = 30 × (10/(R1 + 10))
=> 20 = 300/(R1 + 10)
=> R1 + 10 = 15
=> R1 = 5 Ω