Voltage Divider Formula, Definition, Solved Examples

Voltage Divider Formula: A voltage divider serves as a circuit designed to produce a fraction of the input voltage as its output. Typically constructed with two resistors connected in series and a voltage source, the input voltage is applied across these resistors. Also referred to as a potential divider, it transforms a higher input voltage into a lower value. This arrangement consists of resistors or capacitors that can be tapped at various points in the circuit, allowing for the creation of a precise proportion of the applied voltage between its ends.

Voltage Divider Formula

V _out ​ = ​ V _in ​ ×R ₂ / (R ₁ ​ +R ₂ ) ​ ​

where, V out ​ is the output voltage, V in ​ is the input voltage, R ₁ ​ is the input resistor, R ₂ ​ is the output resistor.

Derivation of Voltage Divider Formula

Consider the circuit depicted below:

Voltage drop across R ₁ ​ is V ₁ ​ . Voltage drop across R ₂ ​ is V ₂ ​ . Input voltage (  V) = V ₁ ​ +V ₂ / 2 ​ .

According to Ohm's law,

V ₁ ​ =I⋅R ₁ ​ …(1)

V ₂ ​ =I⋅R ₂ ​ …(2)

Also,

V=I⋅R eq

V=I⋅(R ₁ ​ +R ₂ ​ )

I= ​ V /(R ₁ ​ +R ₂ )​ …(3)

Substituting (3) into (1) and (2) gives,

V ₁ ​ =​ V ⋅ R ₁ / ​ ​( R ₁ ​ +R ₂ )

V ₂ ​ = V ⋅ R ₂ ​/ ​( R ₁ ​ +R ₂ )

Voltage Divider Formula Solved Examples

Example 1: Calculate the output voltage of a voltage divider circuit with resistors of 5 Ω and 8 Ω, and an input voltage of 20 V. The resistor 8 Ω is in parallel to the output voltage.

Solution: Given: R ₁ ​ =5

R ₂ ​ =8

V _in ​ =20

Using the Voltage Divider Formula: V _out ​ =20×( 8 / 5+8 ​ )

= 20 × 8/13

≈12.31V

Example 2: Calculate the output voltage of a voltage divider circuit with resistors of 6 Ω and 10 Ω, and an input voltage of 30 V. The resistor 10 Ω is in parallel to the output voltage.

Solution: Given: R ₁ ​ =6

R ₂ ​ =10

V _in ​ =30

Using the formula:

V _out ​ =30×( 10 / 6+10 ​ )

= 30 × 10 / 16

V =18.75V

Example 3: Calculate the input voltage of a voltage divider circuit with resistors of 8 Ω and 12 Ω, and an output voltage of 24 V. The resistor 12 Ω is in parallel to the output voltage.

Solution: Given: R ₁ ​ =8

R ₂ ​ =12

V _out ​ =24

Using the formula:

24=V _in ​ ×( 12/8+12 ​ )

24 = V _in ​ ×   3/5 ​

V _in ​ = 120 /3  ​

V _in ​ =40V

Example 4: Calculate the input voltage of a voltage divider circuit with resistors of 3 Ω and 6 Ω, and an output voltage of 9 V. The resistor 6 Ω is in parallel to the output voltage.

Solution: Given: R ₁ ​ =3

R ₂ ​ =6

V _out ​ = 9

Using the formula: V _in ​ ×( 6 / 3+6 ​ )

9 = V _in ​ × 2 / 3​

V in ​ = 27/2 ​

V _in ​ =13.5V

The voltage divider formula, V _out ​ = V _in ​ ×R ₂ ​/ (R ₁ ​ +R ₂ ​) ​ , is a fundamental expression used to calculate the output voltage in a voltage divider circuit. This formula is derived from the principles of Ohm's law and is applicable when two resistors, R ₁ ​ and R ₂ ​ , are connected in series across an input voltage, V in ​ . The output voltage, V out ​ , is determined by the ratio of R ₂ ​ to the total resistance ( R ₁ ​ +R ₂ ​ ), providing a means to obtain a specific fraction of the input voltage in electronic circuits. This formula is versatile and widely used in electronics for designing and analyzing voltage divider circuits.

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