Ans. In using the instrument, after the needle has been set to zero, the current is sent through the coil, producing a deflection of the needle. The coil is then rotated to follow the motion of the needle, the current being kept constant, the rotation being continued until the zero on the upper dial again registers with the needle. The current then is proportional to the sine of the angle through which the coil has been turned, as determined by the lower dial.
Ques. Has the sine galvanometer a large range?
Ans. For a given controlling field, it does not admit of a very large range of current measurement, since, for large deflection, on rotating the coil the position of instability is soon reached.
TABLE OF NATURAL SINES AND TANGENTS
| Angle | Sin. | Tan. |
| 0° | .0000 | .0000 |
| 1 | .0175 | .0175 |
| 2 | .0349 | .0349 |
| 3 | .0523 | .0524 |
| 4 | .0698 | .0699 |
| 5 | .0871 | .0875 |
| 6 | .1045 | .1051 |
| 7 | .1219 | .1228 |
| 8 | .1392 | .1405 |
| 9 | .1564 | .1564 |
| 10° | .1736 | .1763 |
| 11 | .1908 | .1944 |
| 12 | .2079 | .2126 |
| 13 | .2250 | .2309 |
| 14 | .2419 | .2493 |
| 15 | .2588 | .2679 |
| 16 | .2756 | .2867 |
| 17 | .2924 | .3057 |
| 18 | .3090 | .3249 |
| 19 | .3256 | .3443 |
| 20° | .3420 | .3640 |
| 21 | .3584 | .3839 |
| 22 | .3746 | .4040 |
| 23 | .3907 | .4245 |
| 24 | .4067 | .4452 |
| 25 | .4226 | .4663 |
| 26 | .4384 | .4877 |
| 27 | .4540 | .5095 |
| 28 | .4695 | .5317 |
| 29 | .4848 | .5543 |
| 30° | .5000 | .5774 |
| 31 | .5150 | .6009 |
| 32 | .5299 | .6249 |
| 33 | .5446 | .6494 |
| 34 | .5592 | .6745 |
| 35 | .5736 | .7002 |
| 36 | .5878 | .7265 |
| 37 | .6018 | .7536 |
| 38 | .6157 | .7813 |
| 39 | .6293 | .8098 |
| 40° | .6428 | .8391 |
| 41 | .6561 | .8693 |
| 42 | .6691 | .9004 |
| 43 | .6820 | .9325 |
| 44 | .6947 | .9657 |
| 45 | .7071 | 1.0000 |
| 46 | .7193 | 1.0355 |
| 47 | .7314 | 1.0724 |
| 48 | .7431 | 1.1106 |
| 49 | .7547 | 1.1504 |
| 50° | .7660 | 1.1918 |
| 51 | .7771 | 1.2349 |
| 52 | .7880 | 1.2799 |
| 53 | .7986 | 1.3270 |
| 54 | .8090 | 1.3764 |
| 55 | .8192 | 1.4281 |
| 56 | .8290 | 1.4826 |
| 57 | .8387 | 1.5399 |
| 58 | .8480 | 1.6003 |
| 59 | .8572 | 1.6643 |
| 60° | .8660 | 1.7321 |
| 61 | .8746 | 1.8040 |
| 62 | .8829 | 1.8807 |
| 63 | .8910 | 1.9626 |
| 64 | .8988 | 2.0503 |
| 65 | .9063 | 2.1445 |
| 66 | .9135 | 2.2460 |
| 67 | .9205 | 2.3559 |
| 68 | .9272 | 2.4751 |
| 69 | .9339 | 2.6051 |
| 70° | .9397 | 2.7475 |
| 71 | .9455 | 2.9042 |
| 72 | .9511 | 3.0772 |
| 73 | .9563 | 3.2709 |
| 74 | .9613 | 3.4874 |
| 75 | .9659 | 3.7321 |
| 76 | .9703 | 4.0108 |
| 77 | .9744 | 4.3315 |
| 78 | .9781 | 4.7046 |
| 79 | .9816 | 5.1446 |
| 80° | .9848 | 5.6713 |
| 81 | .9877 | 6.3138 |
| 82 | .9903 | 7.1154 |
| 83 | .9925 | 8.1443 |
| 84 | .9945 | 9.5144 |
| 85 | .9962 | 11.43 |
| 86 | .9976 | 14.30 |
| 87 | .9986 | 19.08 |
| 88 | .9994 | 28.64 |
| 89 | .9998 | 57.29 |
Ques. What is the position of instability?
Ans. The position of the needle beyond which the rotation of the coil will cause it to turn all the way round.
Ques. How may the range be increased?
Ans. By an adjustable controlling field or a shunt.
Ques. What advantage has the sine galvanometer over the tangent instrument?