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# Voltage Divider Calculator

### Introduction to Voltage Dividers

Resistors are in series when the same current flows through them. Consequently, by Ohm’s Law, the total voltage in a circuit of series resistors is the sum of the individual drops on the resistors.

$V_T=V_{R1}+V_{R2}$

Another way of saying this is that each resistor contributes to the total voltage in the circuit.

Normally, current must be known to determine voltage drop in a single resistor. Each resistor contributes a voltage drop and that drop is proportional to its resistance. Thus, any voltage drop in a series circuit, given only the resistances and total voltage is solvable.

The voltage node VO in the circuit above is the voltage across R2.

Here’s a way to solve for voltage VO:

$V_T=I_{T}R_{1}+I_{T}R_{2}$

$V_T=I_{T}(R_{1}+R_{2})$

$I_T=\frac{V_{T}}{(R_{1}+R_{2})}$

Since in a series circuit, the total current is equal to the current in each resistor,

$I_{R2}=\frac{V_{T}}{(R_{1}+R_{2})}$

And so,

$\frac{V_{R2}}{R_{2}}=\frac{V_{T}}{(R_{1}+R_{2})}$

finally,

${\color{Red} \mathbf{V_0=V_{R2}=\frac{R_{2}V_{T}}{(R_{1}+R_{2})}}}$

The above equation is known as a voltage divider.

You can easily modify this equation to solve for the voltage across R1: just replace R2 in the numerator with R1.

### Practical Examples

#### Sensor Scaling

Voltage dividers are common for scaling down voltages to safe levels. For example, a sensor whose voltage range is from 0 to 9 V damages most microcontrollers.

A voltage divider circuit in between the sensor and microcontroller, preferable two resistors equal in value, can solve this problem. Why two equal values? because if the two resistors are equal in a voltage divider, then the output voltage is half of the input voltage.

$V_O=\frac{R_{1}V_{T}}{R_1+R_1} \; \; \; R_2 = R_1$

$V_O=\frac{R_{1}V_{T}}{2R_1}$

$V_O=\frac{V_{T}}{2}$

#### Resistance to Voltage Conversion

Another great use of a voltage divider is resistance-to-voltage conversion. Consider a photocell whose resistance varies with light intensity. A microcontroller wouldn’t be able to read the resistance of the photocell directly. But if the photocell is wired as one of the branches in a voltage divider, then its resistance is converted into voltage.

### Voltage Divider Calculator

This online calculator will compute the output voltage in the voltage divider circuit below. Place the input or total voltage value, resistance values and click “Compute”.

Volts (V)

Volts (V)

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