Measuring a Resistance with the Wheatstone-Bridge

Make the connections as shown in fig. 65. Be sure that the binding screws are everywhere tight and that the copper wires are clean and bright at all points where there are contacts. This is especially necessary for the wires which connect R to the box. Any resistance due to them or their contacts will of course be added to the value of R. For delicate measurements contacts must be made by means of thick copper rods amalgamated with mercury, and dipping into mercury cups. The bottoms of the cups should be covered with discs of amalgamated copper, and the wires must press on to these with a steady pressure throughout the experiment; it is not sufficient, to make the contact through the mercury by letting the wires drop into it without touching the copper bottom. The cups themselves are conveniently made of pill boxes, covered with a good thick coat of varnish.

See that all the plugs are in their places in the box, and press them firmly in with a screw motion to ensure efficient contact.

Bring the control magnet of the galvanometer down near the coils, and if the resistance to be measured be not even approximately known, it generally saves time to shunt the galvanometer, using the shunt, provided there be one, if not, a piece of thin German-silver wire. Take two equal resistances out of the arms P and Q. Since it is probable that the galvanometer will be somewhat too sensitive even when shunted, it is better to take out the two 100 ohm plugs rather than the two 10 ohms. Then, since P = Q, R will be equal to S.

Take 1 ohm out from S. Make contact first with the battery key K, and then with the galvanometer key K', and note the direction of the deflexion - suppose it be to the right.

Take out 1000 ohms from S, and note the deflexion - suppose k be to the left. The resistance is clearly between 1 and 1000 ohms.

Now take out 500 ohms - let the deflexion be to the left - R is less than 500. Proceed thus, and suppose that with 67 ohms the deflexion is to the left, and that with 66 ohms it is to the right. The resistance R is clearly between 66 and 67 ohms.

Now make P 10 ohms and- Q 100, and at the same time remove the shunt, and raise the galvanometer magnet to increase the sensitiveness. Since Q is ten times P, S must be ten times R to obtain a balance. Thus S must be between 660 and 670. Suppose that it is found that with 665 ohms the deflexion is to the left, and with 664 it is to the right, the true value of S is between 664 and 665, and since R = PS/Q, the true value of R is between 66.4 and 66.5. We have thus found a third figure in the value of R.

Now make Q 1.000 ohms and P 10 ohms. Then, since Q is 100 times P, S must be 100 times R to secure the balance; and it will be found that when S is 6640 the deflexion is to the right; when it is 6650 it is to the left. The galvanometer may now be made as sensitive as possible; and it will probably be found that with a value of s, such as 6646, there is a small deflexion to the right, and with S equal to 6647 a small deflexion to the left Thus the value of R is between 66.46 and 66.47.

If the fourth figure be required correctly, we may find it by interpolation as follows:

When S is 6646 let the deflexion to the right be a scale divisions, and when it is 6647 let it be b divisions to the left. Then since an addition of 1 ohm to the value of R alters the reading by a+b scale divisions, it will require an addition of a/(a+b) ohms to alter it by a divisions. Thus the true value of R is 6646+a/(a+b) ohms, and the value of S is

The exactness to which the determination can be carried will depend on the accuracy with which the small outstanding deflexions a and b can be read, and on the constancy of the battery.

If it be found that the resistance R is less than 1 ohm, make P 100 ohms, and Q 10; then the value of S will be ten times that of R, and if we find that S lies between 5 and 6, it follows that R is between 0.5 and 0.6; then make P 1000 ohms, and Q 10, and proceed similarly.

After making the determination the connecting wires must all be removed from the box and the plugs replaced.

Experiment. - Determine the values of the resistances in the given box.

Enter results thus: