Measurement of Voltages, Currents and Resistances (Contd)

This is the simplest form of wheatstone bridge and is specially useful for comparing resistances more accurately. The construction of the metre bridge is as shown in the below figure.

It consists of one metre resistance wire clamped between two metallic strips bent at right angles and it has two points for connection. There are two gaps; in one of them a known resistance whose value is to be determined is connected. The galvanometer is connected with the help of jockey across BD and the cells is connected across AC. After making connections, the jockey is moved along the wire and the null point is obtained. The segment of length l₁ and (100-l₁) form two resistances of the wheatstone bridge, the other two reistances being R and S. The wire used is of uniform material and cross-section. The resistance can be found with the help of the following relation

where s is the resistance per unit length of the wire and l₁ is the length of the wire from one end where null point is obtained. The bridge is most sensitive when null point is somewhere near the middle point of the wire. This is due to end resistances.

Sub Topics

End Correction
Potentiometer

End Correction

Sometimes at the end points of the wire, some length is found under the metallic strips and as a result, in addition of length l₁ or (100 - l₁), some additional length should be added for accurate measurements. The resistance due to this additional length is called end resistance. If the end resistance is small, it can be determined by first introducing known resistances P and Q in the gap and obtaining the null point reading l₁, then interchanging P and Q and obtaining the null point reading l₂. Let a and b be the lengths on the respective end under the metallic strips, then we have

Solving the equations (1) and (2) for a and b, we have

Hence the values of a, b can be calculated and suitably accounted for when accurate measurements are required.

Potentiometer

This instrument is identical to the meter bridge except that in this case, the resistance wire is of more than a meter length. This enables greater accuracy. A standard cell of emf e₁ maintains a constant current throughout the wire. As the wire is of uniform material and cross section, it has uniform resistance per unit length. The potential gradient, i.e., r, depends upon the current in the wire.

If an emf e₁ is balanced against the length, say, l₁ we have

Similarly, if another emf e₂ is balanced against the length, say, l₂, we have

From equations (1) and (2), we have

From the above figure, by means of a battery B and rheostat R_h, a steady current is passed through the potentiometer wire AC. Two cells e₁ and e₂ whose emf's are to be compared are put in such a way that positive terminals are connected to A and negative terminal to the galvanometer through a two-way plug key k.

First the cell e₁ is connected by connecting 1 and 3 points of key K₂ and by moving the jockey K on the potentiometer wire, the no deflection point is obtained. Let the reading be l₁, then

where r is the potential gradient and l₁ is the length CN. After this, the points 2 and 3 of the key K₂ are connected i.e., the cell of emf e₂ is put into the circuit and again the no deflection point on the wire is obtained. Let this reading be l₂. Then

e₂ = rl₂

Different sets of observations are taken by varying the variable resistance R_k and then mean value of ratio is computed.