**Question 6: What is wheat stone bridge? Explain with diagram the balancing, the principle and the working of this bridge.**

ANSWER

### Wheatstone Bridge

It is one of the most convenient, precise and widely used instrument for measuring the unknown resistance.

This bridge was first proposed by an English telegraph engineer, Charles Wheatstone. It consists of a battery, Galvanometer and two fixed resistances R_{1} and R_{2} and one variable resistance R_{3} and the unknown resistance R_{x} which is to be found. The schematic diagram is shown below.

ABC and ADC are the two branches and the galvanometer circuit is the bridge across them. The battery is connected between points A and C and the galvanometer between B and D.

### Balancing Principle and working theory

The principle of Wheatstone bridge is that if R_{1}/R_{2} = R_{3}/R_{x}, then the bridge will be in balance conditions and no current will pass through the galvanometer.

In the given circuit unequal currents will flow between the two branches, depending upon the resistances of the branch resistors. The galvanometer will show a deflection. However, adjusting the variable resistance R_{3}, the current in the galvanometer can be made zero. At this stage, the potential difference between A and B will be identical as that of potential difference between A and D. Therefore, points B and D will be at same potential and hence no current will be flowing through the galvanometer. Similarly, the potential difference between C and D is identical as Potential difference between C and B.

Suppose I_{1} is the current flowing in resistors R_{1 }and R_{2} and I_{2} is the current flowing in R_{3} and R_{x}, then, under such balanced conditions,

I_{1}R_{1 }= I_{2}R_{3} and I_{1}R_{2} = I_{2}R_{x}

Now dividing the second equation by the first one;

Thus the unknown resistance can be calculated.

This equation also implies that, R_{1}/R_{2} = R_{3}/R_{x} which verifies the principle of the galvanometer.

Equation (1) can be used to find the unknown resistance R_{X} when it is connected in the circuit in the proper place.

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