Study of Wheatstone Bridge & Kelvin�s Bridge
Aim:- To study the Wheatstone Bridge and measure the unknown resistance.
Apparatus:- Wheatstone Bridge, Kelvin�s Bridge, resistors, galvanometer, etc.
Theory:-
A very important device used in the measurement of medium resistances is the Wheatstone Bridge. A Wheatstone Bridge has been in use longer than almost any electrical measuring instrument. It is still an accurate and reliable instrument and is extensively used in industry. The Wheatstone Bridge is an instrument for comparison measurements and operates upon a null indication principle. This means the indication is independent of the calibration of the null indicating instrument or any of its characteristics. For this reason, very high degrees of accuracy can be achieved using Wheatstone Bridge. Accuracy of 0.1 % is quite common with a Wheatstone bridge as compared to accuracies of 3 % to 5 % with ordinary ohmmeter for measurement of medium resistances. Fig. shows basic circuit of a Wheatstone bridge. It has four resistive arms, consisting of resistances P,Q,R & S together with a source of emf (a battery) and a null detector , usually a galvanometer depends on the potential difference between points c & d. the bridge is said to be balanced when there is no current through the galvanometer or when potential difference across the galvanometer is zero. This occurs when the voltage from the point 'b' to 'a' equals the voltage from point 'd' to point 'b'; or, by referring to the other battery terminal ,when the voltage from point 'd' to point 'c' equals the voltage from point 'b' to point 'c'.
For bridge balance, we can write :
For the galvanometer current to be zero, the following conditions also exist :
and
where
combining eqns. & and simplifying, we obtain:
from which
eqn. is the well known expression for the balance of Wheatstone Bridge. If these resistances are known, the fourth may be determined from eqn. & we obtain :
where R is the unknown resistance S is called the 'standard arm' of the bridge and P & Q are called the 'ratio arms'.
In the industrial and laboratory of the bridge, the resistors make up P,Q & S are mounted together in a box , the appropriate values being selected by dial switches, Battery and galvanometer switches are also included together with a galvanometer and a dry battery in portable sets. P & Q normally consist of four resistors each, the value being 10, 100, 1000 & 10,000 ohm respectively. S consist of a 4 dial or 5 dial decade arrangement of resistors. Fig. shows the commercial form of Wheatstone Bridge.
Limitations of Wheatstone Bridge.
The use of Wheatstone Bridge is limited to the measurement of resistances ranging from a few several megaohm. The upper limit is set the reduction and sensitively to unbalance caused by high resistance values. The upper limit can be extended to a certain extended by increasing the emf applied to the bridge. In this case care has to be taken to avoid overheating of any arm of the bridge. Inaccuracy may also be introduced on account of leakage over insulation of bridge arms when measuring very high resistances. For measurement of very high resistances.
Kelvin double Bridge Method Measurement of Low Resistances.
The Kelvin bridge is a modification of the Wheatstone Bridge and provides greatly increased accuracy in measurement of low value resistances. An understanding of the Kelvin bridge arrangement may be obtained on account of the resistance of the leads and the contact resistances while measuring low valued resistors.
Consider the bridge circuit shown in fig , where ' r ' represents the resistances of the lead that connects the unknown resistance R to standard resistance S. Two galvanometer connections indicated by dotted line, are possible. The connection may be either to point 'm' or to point 'n' . When the galvanometer is connected to point 'm' the resistance, r , of the connecting leads is added to the standard resistance, S, resulting in indication of too low an indication for unknown resistance R. , when the connection is made to point n, the resistances 'r ' is added to unknown resistance resulting in indication of too high a value of for R.
Suppose that instead of using point m, which gives a low result , or n, which makes the result very high, we make the galvanometer connection to any intermediate point 'd' as shown by full line in fig. . if at point 'd' the resistance r is divided into two parts , r1 & r2 such that.
then the presence of r1 the resistance of connecting leads, causes no error in the result . We have,
or,
we can write
Observation Table:
Conclusion: The Kelvin�s bridge is used for measuring very low resistance ranging from 1 ohm to as low as 0.00001 ohm. In this bridge, resistance Rs is represented by the variable standard resistance and the ratio arm (R1 + R2) and it can be usually switched in a number of decade steps. The ratio R1/R2 should be so selected that the relatively large number of the standard resistors is used in the measuring circuit. Thus, the value of unknown resistance Rx can be determined with improved accuracy.