SECTION LXI.

MEASUREMENT OF THE RESISTANCE OF A
GALVANOMETER.

KELVIN'S METHOD.

Apparatus required: Galvanometer, Post Office resistance box, Leclanché cell, resistance box of 1000 ohms and connecting wires.

If the four arms of the resistance bridge (Fig. 108, p. 290) satisfy the relation P/Q = R/S there is no difference of potential between the points A and B, and if they are directly connected by a wire, no current will pass through it. Hence the introduction of such a wire would not alter the strength of the current in any of the arms of the bridge. Conversely, we may conclude that if the current in any one of the branches is the same whether A and B are directly connected together or not the above relation is satisfied. If the branch R contains a galvanometer, the deflection of which serves to indicate the strength of the current through it, we may judge whether the resistances are balanced or not by making and breaking the contact of a wire connecting A and B. If the deflection is the same in both cases the resistance in the branch R must be equal to PS/Q and may therefore be determined without the assistance of a second galvanometer between A and B.

The above considerations lead to an interesting and useful method of determining the resistance of a galvanometer. To obtain accurate results it is in general necessary to send through the instrument a current which under ordinary circumstances would drive the spot of light off the scale. Reducing the sensitiveness of the galvanometer so as to make the deflection measurable would not get over the difficulty, because the test itself would become less sensitive. It is possible

however to work with a large deflection and yet have the spot of light on the scale, because the zero reading of the galvanometer is not required and may therefore be outside the limits of the scale. In the case of a galvanometer of the suspended needle type, it is convenient to begin by deflecting the needle till the spot of light is at the end of the scale by means of a weak magnet arranged so as to alter the direction of the field at the needle without increasing its strength. The battery is then connected to a resistance r (Fig. 113, p. 306) so that only a portion of the current passes through the bridge, the spot of light is brought on to the scale by adjustment of the resistances r and r1. r, is then increased, and the magnet moved so that it still brings the spot of light on to the scale without materially increasing the strength of the magnetic field at the galvanometer needle.

In the case of a D'Arsonval galvanometer, it is only necessary to rotate the whole instrument through an angle of about 30° and to adjust r and r1, until the spot of light appears on the scale.

When the resistance Q of the bridge may be made smaller than the resistance of the galvanometer, the best arrangement is to have Q as small as possible, and P as large as it can be without R being caused to exceed the maximum resistance available in the arm AD. The battery should come between the points A and B, i.e., the battery and short circuiting wire in the figure should be interchanged. When the lowest available resistance of Q is larger than the galvanometer resistance, Q and P should be made equal to each other and as large as possible, and the battery should then be connected as shewn in the figure. If the resistance of the galvanometer is not even approximately known the last-mentioned arrangement is the most suitable and the sensitiveness will generally be sufficient.

In the following exercise, it is required to measure the resistance of a d'Arsonval galvanometer, the method for other galvanometers only differing as explained above in the means adopted to alter the zero reading.

Make connections as shewn in the figure. With r1 small and large, pass a current of short duration through the

S. P.

20

galvanometer by pressing down the key K for an instant.

Turn the galvanometer through an angle of about 30° or 40° in the opposite direction to that in which the spot of light moved on making contact.

=

=

D

Fig 113.

With P Q R = 1000 close the battery circuit at the key K, and adjust r1 and r until the spot of light is on the scale. This is done most rapidly by watching the galvanometer mirror itself instead of the spot of light. Press the short circuiting key K, and observe the side to which the spot of light moves. Then make R = 5000 and repeat the observation. If the motion is in the same direction as the first it indicates that S lies below 1000 or above 5000. The first supposition being the more probable in the present case, repeat the observation with R = 500.

Proceed as in Section LVIII. to find the value of R for which the spot of light does not move when the key K1 is closed.

If no value of R satisfies this condition, find the values differing by unity, for which the deflections are in opposite directions. Determine these deflections and find the value of R for accurate balance by interpolation.

If the resistance of the galvanometer is greater than the lowest available resistance of Q, which will be 10 with the resistance boxes in common use, connect the short circuiting wire to C and D through K,, and the battery circuit to A and B through K1. Make Q10 and P1000 if a resistance of 100 S can be placed in the arm AD, otherwise make P = 100. Take out of the branch AD the resistance which according to the previous determination should produce balance; and if there is a deflection proceed to improve your result. When the balance is nearly perfect stop the current and wait a few minutes in order to allow the galvanometer coil to take up the temperature of the room, it having probably been heated by the passage of currents sufficiently to affect its resistance sensibly. Then repeat the observations.

The battery and short circuit were now interchanged and with Q=10, P=100 it was found that R=2154 gave a balance but that this resistance seemed slowly to increase owing no doubt to the heating of the current. The same result was obtained after waiting five minutes. Hence for the final result:

Resistance of galvanometer C. = 2154
Temperature

= 15°4 C.

SECTION LXII.

DETERMINATION OF THE RESISTANCE OF A CELL.

LODGE'S MODIFICATION OF MANCE'S METHOD.

Apparatus required: Daniell and Leclanché cells, Post Office resistance box, high resistance galvanometer.

=

If in the resistance bridge arrangements (Fig. 108, p. 290) the relation PS QR is satisfied, the arms of the bridge CD and AB are said to be conjugate to each other. No electromotive force in one of these arms will produce a current in the other, and no change of resistance in one of them will modify any current in the other produced by electromotive forces in one or more of the branches of the bridge.

This fact was first used by Mance to determine the resistance of a cell. He placed the cell in one of the arms, and replaced the battery, which in the ordinary resistance bridge supplies the current, by a simple key K, (Fig. 114). Owing to the presence of the cell in BD

=

2

A

D

C

Fig. 114.

K,

S

a current passes through the galvanometer, but when P/Q R/S this current should be the same whether the contact at K2 is open or closed.

Mance's method in its original form has several disadvantages. A comparatively large current has to be sent through the galvanometer, and the key K, has to be pressed down for a time equal to one quarter at least of the period of the galvanometer suspension, so as to allow the first deflection to be read. This may affect the galvanometer injuriously, and it also produces disturbing effects in the cell itself. The closing of the circuit at K2, though it does not affect the current in the