We use this type of bridge for measuring medium range resistances. The **Wheatstone Bridge** measures an unknown resistance by comparing it with a known resistance. **Charles Wheatstone** developed this bridge circuit.

## Wheatstone Bridge Circuit

Here, four resistances P, Q, R and X form a square ABCD as shown in the figure below. The resistance P and Q are adjustable resistances. The resistance R has a known value. Now X is the resistance whose value we have to measure by using the **Wheatstone Bridge circuit**. Now we connect one galvanometer along with a switch in series with it in between B and D. Also we will connect one battery in between A and C along with another switch.

### Operation of Wheatstone Bridge Circuit

In practical **Wheatstone Bridge Circuit**, we can adjust both P and Q at 1, 10, 100, 1000 Ω in steps. After adjusting the value of P and Q at any of the four values, we will connect the battery to the circuit by closing switch S_{1}. As a result, there will be a current flowing through the galvanometer. By pressing the spring switch S_{2} of the galvanometer we can find the non-zero current flowing through this branch of the **Wheatstone Bridge**. Now we have to adjust the resistance R, to reach in such a condition when no current will flow through the galvanometer. That means the circuit has come to a balanced condition.

At this condition, the ratio of P Q is exactly equal to the ratio of R X. We already know the value of the ratio of P to Q. Since, the beginning of the measurement we have ourselves fixed the value of P and Q. Again we have adjusted the value of R. So we also know the value of R. So we can easily find out the value of unknown resistance X.

## Theory of Wheatstone Bridge

Theory of the bridge is quite simple. Let us consider at the balanced condition the current I_{1} is flowing through the resistance P and Q. At the same time current I_{2} is flowing through resistance R and X. Scene, at the balanced condition, Galvanometer detects zero current, there will not be any voltage difference between point B and D. Now the potential at point B in respect of point A is PI_{1}. At the same time, the potential of point D in respect of point A is RI_{2}. We have already told that the potential of point B is exactly equal to the potential of point D. Since there is no voltage difference between point B and D. Hence, we can write

In the same way, the potential of point B in respect of point C is QI_{1}. And the potential of point D point in respect of point C is XI_{2}. For the same previously mentioned reason we can write

Dividing the above two equations, we get,

### Measurement of Resistance with Wheatstone Bridge

The **Wheatstone Bridge** can measure the resistance from 1 Ω to 1 kΩ with much accuracy.

- We generally repeat the measurement of the same unknown resistance with different P to Q ration. As per our standard practice, we generally repeat the measurement with 1:1, 100:10, 1000:10 ration.
- Also sometimes we interchange the position of battery and galvanometer during this measurement. Because this type of measuring instrument works equally well after an alteration of the position of battery and galvanometer.

Repetitions of measurement with changing P to Q ration and also with an alteration of the position of the battery and the galvanometer help us to get the more accurate value of the unknown resistance.

### Applications of Wheatstone Bridge

- A post office box apparatus mainly consists of a Wheatstone bridge circuit.
- We conduct Murray loop test and Varley loop test for finding out the fault in underground cable on the basis of the Wheatstone bridge principle.

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