# Wheatstone Bridge Calculator

Created by Purnima Singh, PhD
Reviewed by Steven Wooding
Last updated: Nov 01, 2022

Omni's Wheatstone bridge calculator allows you to determine the unknown resistance in a Wheatstone bridge circuit. You can use this calculator for both balanced and unbalanced Wheatstone bridges.

Continue reading to know what the Wheatstone bridge is and how to calculate resistance using the Wheatstone bridge equation. You will also find some of its applications in electronic systems.

## What is a Wheatstone bridge?

The Wheatstone bridge is a circuit that measures unknown electrical resistance. It is basically a rhombus-shaped network of four resistance arms connected to an external voltage source (see figure 1). The circuit gets its name because it was developed by Charles Wheatstone, and a bridge joins the resistor arms.

The Wheatstone bridge circuits are commonly used in electronic sensors to precisely detect small changes in resistances. In fact, most strain gauges use the Wheatstone bridge circuits.

🙋 Another bridge circuit that is commonly used in electronic circuits to convert AC supply voltage to DC is the bridge rectifier. You can learn more about it from the bridge rectifier calculator.

## Circuit of Wheatstone bridge

Figure 1 shows the circuit of a Wheatstone bridge. The resistors $R_1$ (arm AD) and $R_3$ (arm AB) have a fixed value, whereas, the resistor $R_2$ (arm DC) is variable. The unknown resistance $R_x$ is connected in arm BC.

The resistances $R_1$ (arm AD) and $R_2$ are connected in series and make one voltage divider circuit. The same goes for the resistances $R_3$ (arm AD) and $R_x$, which make the second voltage divider circuit. These two series combinations of resistors are then connected in a parallel arrangement. For a quick reminder of the various resistor combinations, check out the series resistor calculator and parallel resistor calculator.

We can measure the output of the Wheatstone bridge between terminals B and D by using a device called a galvanometer.

## Wheatstone bridge formula

With a supply voltage $V$ applied across the bridge, we can write the formula for the output voltage $V_G$ of an unbalanced Wheatstone bridge as:

$\scriptsize V_G = V \left ( \frac{R_1}{R_1+R_2} + \frac{R_3}{R_3+R_x} \right )$

To measure the unknown resistance $R_x$, we need to vary the resistance $R_2$ until the galvanometer gives zero reading. This means that no current flows through the arm DB, as both points D and B are at the same potential. Under this condition, we say that the Wheatstone bridge is balanced.

For a balanced Wheatstone bridge:

$\scriptsize V_G = 0$

Hence, we can modify the unbalanced Wheatstone bridge equation as:

$\scriptsize \frac{R_1}{R_2} = \frac{R_3}{R_x} \\ \text{....or:} \\ R_x=\left ( \frac{R_2}{R_1} \right ) R_3$

A galvanometer is a very sensitive device. Hence, it is possible to make null measurements up to very high precision. As a result, the resistance measurement using the Wheatstone bridge is very accurate (up to four significant figures).

## How to calculate resistance in the Wheatstone bridge?

To understand how to calculate an unknown resistance in the Wheatstone bridge, let us consider an example of a balanced Wheatstone bridge where $R_1 = 6\ \Omega$, $R_2 = 9\ \Omega$, $R_3 = 4\ \Omega$, and $V = 3.0 \ \rm V$.

As the circuit is in a balanced state, i.e., the galvanometer does not show any deflection, we can use the Wheatstone bridge formula:

$\scriptsize \begin{split} \frac{R_1}{R_2} &= \frac{R_3}{R_x} \\ R_x &= \left ( \frac{9\ \Omega}{6\ \Omega} \right ) 4\ \Omega \\ R_x & = 6 \ \Omega \end{split}$

Hence, the unknown resistance is $6 \ \Omega$.

## How to use the Wheatstone bridge calculator?

Now that you know how to calculate resistance in the Wheatstone bridge, let us solve the same problem using the Wheatstone bridge calculator.

1. Using the drop-down menu, select "Value of $R_x$ for balanced bridge".

2. Input the values of known resistances, $R_1 = 6\ \Omega$, $R_2 = 9\ \Omega$, and $R_3 = 4\ \Omega$.

3. The tool will use the Wheatstone bridge equation to calculate the value of the unknown resistance $R_x = 6 \ \Omega$ and display it.

4. In case you want to use the Wheatstone bridge calculator to calculate the voltage across the bridge, $V_G$, you need to enter the values of input voltage and the four resistances $R_1$, $R_2$, $R_3$, and $R_x$.

## FAQ

### What is the Wheatstone bridge principle?

According to the Wheatstone bridge principle, when the bridge is balanced, the resistance of the four arms that form the bridge are proportional to each other, i.e., R₁ / R₂ = R₃ / Rₓ.

### How to calculate the equivalent resistance of the Wheatstone bridge?

To calculate the equivalent resistance of a Wheatstone bridge in a balanced state, follow the given instructions:

1. Add the two sets of resistors in series to get their respective equivalent resistances.
2. Now add the reciprocal of the two equivalent resistances from step 1.
3. Take the reciprocal of the value in step 2.
4. Congrats! You have calculated the equivalent resistance of a Wheatstone bridge.

### What is a Wheatstone bridge used for?

Some common applications of the Wheatstone bridge circuit are:

1. To precisely measure resistances by comparing it with known resistances.
2. For strain measurements to detect any relative change in resistance due to mechanical factors like force, pressure, etc. by using a strain gauge.
3. For temperature measurements by using a thermistor (temperature-sensitive resistor) in place of one of the resistances.

### How much is the output current through a Wheatstone bridge in balanced condition?

Zero. When a Wheatstone bridge is balanced, the potential difference across the output of the bridge is null, hence, the output current through it is also zero.

### How to use the Wheatstone bridge for resistance measurement?

To use the Wheatstone bridge for resistance measurement, proceed as follows:

1. Adjust the value of the variable resistor until the galvanometer shows no deflection.
2. Now, your bridge is in a balanced state, you can determine the value of unknown resistance by using the Wheatstone bridge formula.
3. Multiply the value of the variable resistance by the ratio of the known resistances in the other two arms of the bridge.
4. You have measured the unknown resistance using a Wheatstone bridge!
Purnima Singh, PhD
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