Kelvin double bridge

Kelvin Double Bridge Method of Measurement of Low Resistances

The Kelvin bridge is a modification of the Wheatstone bridge and provides greatly increased accuracy in measuring low-value resistances. An understanding of the Kelvin bridge arrangement may be obtained by a study of the difficulties that arise in a Wheatstone bridge 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 resistance of the lead that connects the unknown resistance R to standard resistance S. Two galvanometer connections indicated by dotted lines, are possible. The connection may be either to point 'm' or to 'n' point. When the galvanometer is connected to point m the resistance, r, of the connecting leads is added to the standard resistance, S, resulting in an indication of too low an indication for unknown resistance R. When the connection is made to point n, the resistance, r, is added to the unknown resistance resulting in an indication of too high a value for R.

Suppose that instead of using point m which gives a low result, or n, which makes the result 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 and r2, such that

Therefore we conclude that making the galvanometer connection as at c, the resistance of leads does not affect the result. The process described above is obviously not a practical way of achieving the desired result, as there would certainly be a trouble in determining the correct point for galvanometer connections. It does, however, suggest the simple modification, that two actual resistance units of correct ratio be connected between points m and n, the galvanometer be connected to the junction of the resistors. 

The Kelvin double bridge incorporates the idea of the second set of ratio arms — hence the name double

bridge — and the use of four terminal resistors for low-resistance arms. The figure shows the schematic

diagram of the Kelvin bridge. The first of ratio arms is P and Q. The second set of ratio arms, p and q is used to connect the galvanometer to a point d at the appropriate potential between points m and n to eliminate the effect of connecting lead of resistance r between the known resistance, R, and the standard resistance, S.

The ratio p/ q is made equal to P/ Q. Under balance conditions there is no current through the galvanometer, which means that the voltage drop between a and b, Eab is equal to the voltage drop Eamd between a and c.

It indicates that the resistance of connecting lead, r, has no effect on the measurement, provided that the two sets of ratio arms have equal ratios. It indicates that it is desirable to keep r as small as possible in order to minimize the errors in case there is a difference between ratios P/Q and p / q.

The effect of thermo-electric emfs can be eliminated by making another measurement with the battery connections reversed. The true value of R being the mean of the two readings.

In a typical Kelvin bridge, the range of resistance covered is 0.1 micro Ohm to 1.0 Ohm.

In this bridge there are four internal resistance standards of 1 Ohm, 0.1 Ohm, 0..01 Ohm and 0.001 Ohm respectively.