# Wheatstone Bridge Calculator

Created by Krishna Nelaturu
Last updated: Nov 05, 2022

Our Wheatstone bridge calculator can help you determine the value of the unknown resistance in a balanced Wheatstone bridge or calculate an unbalanced Wheatstone bridge output voltage. Don't fret if these terms are confounding. Join us below for a brief discussion on Wheatstone bridge, including some fundamentals:

• What is a Wheatstone bridge?
• Unbalanced Wheatstone bridge formula for bridge voltage.
• Balanced Wheatstone bridge equation for unknown resistance.

Reading up on Ohm's law before diving in can be helpful. Our Ohm's law calculator will prove an informative read!

## What is a Wheatstone bridge?

A Wheatstone bridge is a simple circuit used to measure electrical resistance or conductivity. It works by using a set of resistors connected in a specific configuration, with the voltage across the circuit being measured and compared to a calibrated reference.

The Wheatstone bridge consists of two pairs of resistors connected in a series-parallel combination, as shown in the image above. Resistances $R_1$ and $R_2$ are in series, similar to the resistances $R_3$ and $R_x$. These two resistance arms are parallel to each other. A galvanometer measures the voltage across the "bridge" points B and D.

There are many different applications for Wheatstone bridges in the real world. They often find usage in measuring instruments and laboratory equipment, such as electrical resistance meters or conductivity sensors. Wheatstone bridges are commonly found in strain gauges thanks to their high sensitivity.

## How to use a Wheatstone bridge?

A common use of a Wheatstone bridge is to determine the value of an unknown resistor $R_x$. Let's go through the process step-by-step:

1. We acquire two fixed resistances $R_1$ and $R_3$, and a variable resistance $R_2$. We know their resistance at all times.

2. Connect these resistors in the Wheatstone bridge configuration shown in the previous section. We must ensure that

• The resistors $R_1$ and $R_2$ are in series;
• The resistors $R_3$ and $R_x$ are in series; and
• We connect a galvanometer across the "bridge" to measure the voltage.
3. Check the galvanometer. If the reading is zero, move on to step 4. If the reading is non-zero, voltage passes through the bridge, which we call an unbalanced Wheatstone bridge. Vary the resistance of the variable $R_2$ until the galvanometer reads zero and there is no voltage across the bridge.

4. When the galvanometer shows zero, there is no voltage across the bridge. We call this setup a balanced Wheatstone bridge. From this setup, we can easily calculate the unknown resistance. We shall learn how in the balanced Wheatstone bridge formula section.

## Unbalanced Wheatstone bridge output voltage

The bridge voltage in an unbalanced Wheatstone bridge is given by the equation:

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

Where:

• $V_G$ - The bridge voltage;
• $V$ - The input source voltage;
• $R_1, R_3$ - Known fixed resistances;
• $R_2$ - Known variable resistance; and
• $R_x$ - Unknown resistance.

## Balanced Wheatstone bridge formula

In a balanced Wheatstone bridge, $V_G = 0$. Using this in the bridge voltage equation above gives us:

\begin{align*} \frac{R_1}{R_1 + R_2} - \frac{R_3}{R_3 + R_x} =0\\[1.5em] \implies \frac{R_1}{R_1 + R_2} = \frac{R_3}{R_3 + R_x} \end{align*}

Simplifying this, we get the balanced Wheatstone bridge equation for the unknown resistance as:

$R_x = R_3 \cdot\frac{R_2}{R_1}$

## Wheatstone bridge equivalent resistance

The formula for the Wheatstone bridge equivalent resistance $R_{\rm{eq}}$ is:

$R_{\rm{eq}} = \frac{(R_1 + R_2) \cdot (R_3 + R_x)}{R_1 + R_2 + R_3 + R_x}$

Want to understand how we got this equation? Please go through our articles in series resistor calculator and parallel resistor calculator.

## Using this Wheatstone bridge calculator

Our Wheatstone bridge calculator is simple to use:

• Select what you need to calculate. You can:
• Calculate the unknown resistance in a balanced Wheatstone bridge, or
• Calculate the bridge voltage in an unbalanced Wheatstone bridge.
• Enter all the known values. In the case of a balanced Wheatstone bridge, you need to enter three resistance values. In the case of an unbalanced Wheatstone bridge, you must provide the source voltage and the four resistance values.
• The Wheatstone bridge calculator will instantly give you all the unknowns:
• The unknown resistance in a balanced Wheatstone bridge.
• The Wheatstone bridge output voltage in an unbalanced Wheatstone bridge.
Krishna Nelaturu
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