EXPERIMENT 39

39.1Object: Measurement of a Small Resistance by Kelvin’s Double Bridge

Resistance below 1 ohm value is called low resistance. The Kelvin’s double bridge method is the best for a correct measurement of low resistance. The bridge is shown in Figure 39.1.

Figure 39.1

The resistance to be measured is connected between terminals A, B and designated as X.

S is standard resistance of the same order of magnitude as the X.

A small resistance link, r, is used between terminal B and C. Q, M, q, and m are known resistance in which one pair, Q-q or M-n, is variable.

39.2Experimental Setup

When we obtain a balance in a galvanometer by adjusting the variable resistances, the X unknown resistance will be given by

Q/M is kept equal to q/M. The link resistance, r is nearly zero as it is made of thick copper strip. The X will be given by

To take into account the thermoelectric EMF, the measurement should be made with the current direction reversed. The mean of the two measurements should be taken.

We use a battery, two keys, 5 ohm resistance, S variable resistance, a galvanometer, a post office box, and high resistance. After finding out the balance measure, the Q and M (or q and m), whichever were variables on a post office box.

Connect the circuit as shown in Figure 39.1. The bridge circuit can also be drawn as shown in Figure 39.2.

Figure 39.2

39.3Procedure

Select a battery and connect the positive point to one of the post office boxes, S, which is working as the standard resistance. This point is connected to fixed terminal M of resistor MQ. The second point of the post office box is connected to the fixed terminal m of the other resistor mq.

Negative terminal of the battery is connected to a key, and the second point of the key is connected to 5 Ω resistance. The 5 Ω resistance is used to limit current in the low resistance. The resistance to be measured is of the order of 0.001, or even smaller. The high current may destroy the low resistance. A voltage drop takes place in a 5 ohm resistor and the current can be controlled.

The second point of this resistance is connected to one end of unknown resistance X. The same point is connected to the fixed point Q of resistor QM. The second point of X is connected to the fixed point q of resistor qm. The variable point MQ is connected to key K₂. The other point of the key is connected to one terminal of the galvanometer. The high resistance is used with the galvanometer to protect it from high current flow. The other point is connected to a resistor mq as shown.

Some resistance of 0.2 ohm is taken out from the post office box by adjusting the variable points of resistors, and the null position is obtained. Now one point of the MQ resistor (say M) is disconnected from the post office box to determine the value of the M resistance. The variable point of MQ is connected to one point of the post office box, and the value of M is found. The value of Q is also determined. The connections are reversed and M and Q are again determined.

EXPERIMENTAL RESULTS

The mean X = 0.38.

39.4Experiment

An experiment was performed to measure a resistance of 0.38 by Kelvin’s double bridge. Experimental results are presented in tabular form.

39.5Discussion

A Kelvin’s double bridge is used to measure a low resistance of the order of 1 ohm. This is the most accurate method of low resistance measurement.