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# Wheatstone Bridge Calculator

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In simple words Wheatstone bridge acts as a galvanometer and it gives the value of unknown resistance. The diagram represents the Wheatstone bridge is given below:

The formula for unknown resistance and the bridge voltage are,
Unknown resistance formula:
$R_{x}$ = $\frac{R_{b}\times R_{c}}{R_{a}}$

Bridge voltage formula:
$V_{b}$ = $V_{in}\times$ $\left ( \frac{R_{x}}{R_{x}+R_{c}}-\frac{R_{b}}{R_{b}+R_{a}} \right )$

Where,
$R_{a}$, $R_{b}$, $R_{c}$ and $R_{x}$ are resistors in the circuit,
$V_{in}$ is the input voltage,
$V_{b}$ is the bridge voltage.

## Steps

Step 1 : Note down the given parameters of the question.

Step 2 : Plug these values in the formula and find out the required parameters

$R_{x}$ = $\frac{R_{b}\times R_{c}}{R_{a}}$

$V_{b}$ = $V_{in}\times$ $\left ( \frac{R_{x}}{R_{x}+R_{c}}-\frac{R_{b}}{R_{b}+R_{a}} \right )$

## Problems

Some of the solved problems related to wheatstone bridge are given below.

### Solved Examples

Question 1: The input voltage of a Wheatstone bridge circuit is 12V, the three resistors have the resistance 40$\Omega$,30$\Omega$ and 80$\Omega$ respectively. Calculate the unknown resistance $R_{x}$ and the bridge voltage.
Solution:

Given that,
$V_{in}$ = 12V,
$R_{a}$ = 40$\Omega$,
$R_{b}$ = 30$\Omega$,
$R_{c}$ = 80$\Omega$.

Unknown resistance of Wheatstone bridge circuit is,

$R_{x}$ = $\frac{R_{b}\times R_{c}}{R_{a}}$

$R_{x}$ = $\frac{30\times 80}{40}$ = $\Omega$

Bridge voltage can be calculated as,

$V_{b}$ = $V_{in}\times$ $\left ( \frac{R_{x}}{R_{x}+R_{c}}-\frac{R_{b}}{R_{b}+R_{a}} \right )$

$V_{b}$ = 12$\times$ $\left ( \frac{60}{60+80}-\frac{30}{30+40} \right )$ = 3.423$\times10^{-16}$V

Question 2: The input voltage of a Wheatstone bridge circuit is 15V, the three resistors have the resistance 35$\Omega$,20$\Omega$ and 40$\Omega$ respectively. Calculate the unknown resistance $R_{x}$.

Solution:

Given that,
$V_{in}$ = 15V,
$R_{a}$ = 35$\Omega$,
$R_{b}$ = 20$\Omega$,
$R_{c}$ = 40$\Omega$.

Unknown resistance of Wheatstone bridge circuit is,

$R_{x}$ = $\frac{R_{b}\times R_{c}}{R_{a}}$

$R_{x}$ = $\frac{20\times 40}{35}$ = 22.85$\Omega$.