A **Wheatstone Bridge** is an electrical circuit used to measure an **unknown resistance** by balancing two legs(one leg containing the unknown component) of the circuit.

Index

**History**

The Wheatstone bridge was invented by British scientist, physicist and mathematician *Samuel Hunter Christie** *in *1833* and later, improved by English scientist, Sir *Charles Wheatstone** *in *1843*.

**Wheatstone Bridge Explained**

So, let’s dive deep into the explanation of this concept.

**Theory**

The Wheatstone bridge works on the **principle of null deflection**, i.e. the ratio of their resistances are equal, and no current flows through the galvanometer. The bridge is very reliable and gives an accurate result.

The Wheatstone Bridge circuit is nothing more than two simple series-parallel arrangements of resistances connected between a voltage supply terminal and ground producing zero voltage difference between the two parallel branches when balanced.

The circuit has two input terminals(current flowing in, at A, through R_{1} and R_{3}) and two output terminals(current flowing out, at C, through R_{2} and R_{x}) consisting of four resistors configured in a diamond-like arrangement as shown.

**R _{x}** – unknown resistance

**R**,

_{1}**R**,

_{2}**R**– known resistances

_{3}**V**– Voltage source

_{G}In the above figure, R_{x}, R_{1}, R_{3} are fixed resistances, while R_{2} is adjustable resistance. So, R_{2} is adjusted until the bridge is **balanced**, i.e., no current flows through the galvanometer.

At this point, the voltage between B and D will be zero.

This gives,

\(\frac{R_2}{R_1} = \frac{R_x}{R_3}\)

\(⇒ R_x = \frac{R_2}{R_1}.R_3\)

If R_{1}, R_{2}, and R_{3} are known to a high precision, then R_{x} can be calculated to a high precision.

**Derivation**

Initially, **Kirchoff’s First Law** is used at B and D,

\(I_3 – I_x + I_G = 0\)

\(I_1 – I_2 – I_G = 0\)

Using **Kirchoff’s second law** in loops ABDA and BCDB,

\((I_3 . R_3) – (I_G . R_G) – (I_1 . R_1) = 0\)

\((I_x . R_x) – (I_2 . R_2) + (I_G . R_G) = 0\)

Since the bridge is balanced,

\(I_G=0,\\

I_1 = I_2 \mbox{ and } I_3 = I_x\\

⇒ I_3 . R_3 = I_1 . R_1\\

⇒ I_x . R_x = I_2 . R_2\\

⇒ R_x = \frac{R_2.I_2.I_3.R_3}{R_1.I_1.I_x}\\

∴ R_x = \frac{R_2.R_3}{R_1}\\

\)

**Applications of Wheatstone Bridge**

- The wheatstone bridges are used for the
**precise measurement of low resistance**. The**Kelvin bridge, Carey Foster bridge,**etc., was specially adapted from the Wheatstone bridge for measuring very low resistances. - Variations on the Wheatstone bridge can be used to measure
**capacitance, inductance, impedance**and other quantities, such as the amount of combustible gases in a sample, with an explosimeter. - Wheatstone bridges along with an operational amplifiers are used to measure the physical parameters like temperature, strain, light, etc.

**Limitations ****of Wheatstone Bridge**

**of Wheatstone Bridge**

- These wheatstone bridges gives inaccurate readings if it is unbalanced.
- It is a very sensitive device.
- It is used for measuring resistances ranging from a few ohms to a few kilo-ohms.

**Example**

**Question.** In a Wheatstone’s bridge R_{1} = 100 Ω, R_{2} = 1000 Ω and R_{3} = 40 Ω. If the galvanometer shows zero deflection, determine the value of the unknown resistor.

**Solution.** Given, R_{1} = 100Ω, R_{2} = 1000Ω and R_{3} = 40Ω

As we know,

\(R_x = \frac{R_2.R_3}{R_1}\)

\(⇒ R_x = \frac{1000 * 40}{100}\)

\(∴ R_x = 400 Ω\)

**FAQs**

**What is the principle on which Wheatstone bridge operates?**The Wheatstone bridge works on the principle of null deflection, i.e. the ratio of their resistances are equal, and no current flows through the galvanometer.

**What is the Wheatstone bridge formula?**The formula for Wheatstone bridge is,

\(R_x = \frac{R_2.R_3}{R_1}\)

Where,

\(R_x\) – unknown fixed resistor

\(R_1, R_2, R_3\) – known fixed resistors

**State the Kirchoff’s laws.***Kirchhoff’s Current Law* states that, in a circuit, the total of the currents in a junction is equal to the sum of currents outside the junction.*Kirchhoff’s Voltage Law* states that, the sum of the voltages around the closed loop is equal to null.