Question

What is the meter bridge? On which principle does it work? Explaining its construction obtain the expression for determining unknown resistance with the help of meter bridge. Give necessary diagram also.

Answer 1

Meter Bridge:

It is the simplest practical application of the Wheatstone bridge that is used to measure an unknown resistance.

Construction: It consists of usually one meter long Manganin or constant on wire of uniform cross-sectional area, stretched along a meter scale fixed over a wooden board and with its two ends soldered to two L- shaped thick copper strips M and N. Between these two copper strips, another copper strip I is fixed so as to provide two gaps ab and a₁b₁. A resistance box R.B. is connected in the gap ab and the R.B. G
unknown resistance S is connected to the gap ab. and the

unknown resistance S is connected to the gap a₁b₁. A source of emf e is connected across AC. A movable jockey and a galvanometer are connected at BD as shown in figure.

Working: After taking out a suitable resistance R from the resistance box, we touches the jockey at point A and C and observe opposite deflection in galvanometer. If galvanometer shows deflection in one direction then we change the value of known resistance until galvanometer shows opposite deflection.

Now the jockey is moved along the wire AC till there is no deflection in the galvanometer. This is the balanced condition of the Wheatstone bridge. If P and Q are the resistances of the parts AB and BC of the wire, then for the balanced condition of the bridge we have
\(\frac{P}{Q}=\frac{R}{S}\) ……………….. (1)
If resistance of unit length of the wire is \(\sigma \frac{{ohm}}{{cm}}\) and the balance point occurs at l cm from A then the length of part BC will be (100 – l) cm.
P = Resistance of wire of AB part = σl …………. (2)
Q = Resistance of wire of BC part = σ (100 – l) ……………… (3)
In equation (1) putting the value P and Q

Knowing l and R, unknown resistance can be determined.
The formula of determination of specific resistance of unknown resistannce (S)
We know that
Unknown resistance (S) = \(\rho \frac{P'}{A}\)
Where l’ = Length of unknown resistance
A = Area of cross section = πr²
From equation (4)

Limitations of Meter Bridge:

1. Copper strips have their own resistances but in the calculation of meter bridge formula we neglect this resistance so that our results are errorful. For minimising this error, at time of performing experiment we should calculate unknown resistance by interchanging the position of unknown resistance and known resistance. In this process we take average value of obesrvations by which error can be minimised.

2. The resistances of endpoints affect the sensitivity of the meter bridge. To nulify, this effect Carey-Foster s bridge is used.

3. Current should not flow for long time through the wire otherwise wire will heat up and the resistance of wire will be changed.

4. Jockey should not slide tightly on resistance wire otherwise it’s cross-section area will change. That is why the resistance of wire will be changed.