**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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