The meter bridge is another form of Wheatstone’s bridge.

**Meter bridge**

The meter bridge is
another form of Wheatstone’s bridge. It consists of a uniform manganin wire AB
of one meter length. This wire is stretched along a meter scale on a wooden
board between two copper strips C and D. Between these two copper strips
another copper strip E is mounted to enclose two gaps G_{1} and G_{2}
as shown in Figure 2.26. An unknown resistance P is connected in G_{1}
and a standard resistance Q is connected in G_{2}. A jockey (conducting
wire) is connected to the terminal E on the central copper strip through a
galvanometer (G) and a high resistance (HR). The exact position of jockey on
the wire can be read on the scale. A Lechlanche cell and a key (K) are
connected across the ends of the bridge wire.

The position of the
jockey on the wire is adjusted so that the galvanometer shows zero deflection.
Let the point be J. The lengths AJ and JB of the bridge wire now replace the
resistance R and S of the Wheatstone’s bridge. Then

where R′ is the resistance per
unit length of wire

The bridge wire is
soldered at the ends of the copper strips. Due to imperfect contact, some
resistance might be introduced at the contact. These are called end
resistances. This error can be eliminated, if another set of readings are taken
with P and Q interchanged and the average value of P is found.

To find the specific
resistance of the material of the wire in the coil P, the radius r and length *l*
of the wire is measured. The specific resistance or resistivity ρ can be
calculated using the relation

Resistance = ρ . *l/A*

By rearranging the
above equation, we get

If P is the unknown
resistance equation (2.57) becomes,

**EXAMPLE 2.25**

In a meter bridge with a
standard resistance of 15 Ω in the right gap, the ratio of balancing length is
3:2. Find the value of the other resistance.

*Solution*

**EXAMPLE 2.25**

In a
meter bridge, the value of resistance in the resistance box is 10 Ω. The
balancing length is *l*_{1} =
55 cm. Find the value of unknown resistance.

*Solution*

Q = 10 Ω

Tags : Explanation, Formulas, Solved Example Problems | Kirchhoff’s rule and Wheatstone’s bridge , 12th Physics : Current Electricity

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12th Physics : Current Electricity : Meter bridge | Explanation, Formulas, Solved Example Problems | Kirchhoff’s rule and Wheatstone’s bridge

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