## Thursday, August 11, 2016

### Wheatstone bridge and Meter Bridge

Wheatstone bridge

Kirchhoff laws are useful to find the current passing across a element in a electric circuit. We can apply first law that deals with current coming towards a junction is the current leaving the junction. The second law is about conservation of potential difference across a closed circuit. It is easy to apply this laws to a complex circuit and solve the problem.

Wheatstone bridge is a particular arrangement of four resistors with which we can measure the forth resistance if three o them are known to us.

Between two junctions we can connect a galvanometer and we can check the current passing in the circuit. Between the other two junctions, a cell with a known EMF is connected.

We can apply kirchhoff’s second law in each closed loop and find out the equations and we can solve them further. We can apply the law only when the wheatstone bridge is balanced. When it is balanced, the current passing across the galvanometer is zero. In that case the ratio of the resistors is same.

We can derive the condition for the wheatstone bridge using the Kirchhoff laws as shown below with all the conditions and sign conventions.

When the bridge is balanced, we can find as shown below that, the ratio of the resistance of the pairs is same.

Wheatstone bridge is a particular arrangement of four resistors with which we can measure the forth resistance if three o them are known to us.

Problem and Solution

The following problem is about finding the balance of Wheatstone bridge. Four resistors were given in the bridge but the bridge is not balanced. We need to know the resistance to be connected to any one resistor so that the bridge is balanced.

To solve this problem, we simply need to apply the condition for the balanced wheatstone bridge and by simplifying the equation, we can solve the problem as shown below.

Meter bridge

Meter bride is a modified version of wheatstone bridge. There is practical issues in using the wheatstone bridge. The serious problem is getting the balance of the bridge. We can apply the rule only when the circuit is balanced and the galvanometer shows zero deflection. For that to happen, we need to keep changing one resistors keeping the others same.

The balance happens at a particular resistance and we don’t know that value. Finding that value by keep changing the circuit is quire a time consuming and impractical process.

To avoid this problem, two of the resistors were replaced with a wire and jockey. It will divide the wire into two parts and each part has a particular resistance basing on its length.

We can prove that the ratio of the two resistors is the ratio of the lengths of the two parts of the meter wire taken in the experiment.

Problem and solution

We need to solve the resistance of a wire kept in the meter bridge and we are changing the temperature at the other end. So we need to take coefficient of temperature into count and find the value of resistance as shown below.

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