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Int. Sc. 1886.

The terminals of the battery are connected to the electrodes of a reflecting electrometer, and the deflection on the scale is 1oo divisions. What will the deflection be, when, everything else remaining the same, the external circuit is broken ?

137. Describe some form of Thomson's Quadrant Electrometer.

The two poles of a battery are connected to the electrodes of a quadrant electrometer, and readings taken (1) when there is no circuit, (2) when the circuit is completed by a wire of 6 ohms resistance. The mean readings in the two cases being 200 and 147 respectively, determine the resistance of the battery. Prel. Sc. 1888.

138. A battery of Daniell's cells, arranged two abreast, is required to maintain a current of 3 ampères through an external resistance of 2 ohms. How many cells will be required, the E.M.F. of each being 1.2 volt, and the internal resistance of each 0.4 ohm ? Prel. Sc. 1887.

139. A battery is connected by short thick wires to a galvanometer, and the deflection noted. The galvanometer is then shunted with one-third of its own resistance, and on connecting again with the battery the current through the galvanometer is observed to have half its former value. Show that the resistance of the battery is half that of the galvanometer. N. S. Tripos. 1886.

140. The resistance of a shunted galvanometer is 85 ohms, that of the shunt being 100 ohms. A certain deflection of the galvanometer needle is obtained when the resistance in the rest of the circuit is 2000 ohms. Find what additional resistance must be inserted that the galvanometer deflection may remain the same when the shunt is removed.

B. Sc. 1887 141. Define the magnetic moment of a magnet, and state the laws which express the direction and magnitude of the force exerted by an electric current passing along a circular wire upon a magnetic pole at the centre of the circle.

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A battery-cell of constant electromotive force and negligible resistance is connected up with two galvanometers A and B, arranged first in series and secondly in multiple

In the first case the deflection of A is 25 and that of B 46 ; and in the second case that of A is 43. Find the deflection of B, and compare the constants and resistances of the two galvanometers, assuming that the currents in each case are proportional to the deflections.

N. S. Tripos. 1884. 142. Describe the action of an electric current on a magnet, and explain how it is made use of in a galvanometer.

There are 25 turns of wire in a galvanometer coil, the mean radius of which is 150 cm. Assuming the value of H to be 0.18, find the current which will deflect a magnet placed at the centre of the coil 45°. If the resistance of the circuit, including the battery, be 3 ohms, find the electromotive force required to produce the current,

Int. Sc. 1886.

[See p. 214. The current is equal to 0.172 C.G.S. unit or 1:72

ampère, and the required E.M.F. is 172 X 3 = 5.16 volts.]

143. What is meant by the reduction factor of a galvanometer ?

A sine galvanometer .consists of a single coil of 49 turns of wire, the mean radius of which is 20 cm. A current of o8 ampère causes such a deflection that the coil has to be turned through 45° degrees to bring the needle to its original position with regard to the coil. Determine the reduction factor of the galvanometer, and the horizontal component of the earth's magnetic intensity.

Int. Sc. Honours 1887. 144. The terminals of a galvanometer (resistance=G) are connected with a cell (E.M.F.=E,) and resistance Ry, and at the same time with another cell (E.M.F = E2) and resistance R, Determine the current through the galvanometer in terms of the data, and show that by

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suitably adjusting the resistances R, and R, a comparison of the electromotive forces of the cells may be made.

Int. Sc. Honours 1885. 145. State the laws of electrolysis.

A copper voltameter and an acidulated water voltameter are inserted in the same voltaic circuit; and it is found that 1.5 gramme of hydrogen is given off while 47.625 grammes of copper are deposited on the copper cathode. Calculate the atomic weight of copper. [Copper is divalent.]

Oxford (Prel. Sc.) 1887. 146. Describe a series of experiments to prove Ohm's law. A current passes from A to D through a circuit composed as follows : Between A and B is a resistance of i ohm, between B and D an unknown small resistance ; A is joined to C by a resistance of 2 ohms, and B to C by one of 99 ohms. The terminals of an electrometer (or of a high-resistance galvanometer) are joined alternately to A and C and to B and D, and the deflections are the same in the two cases. Find the value of the unknown small resistance.

B. Sc. 1886.

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Between A and B there is a divided circuit, one branch of which

(AB) has a resistance of i ohm, while the other branch (ACB) has a resistance of 101 ohms. If C is the total current, then the current through ACB is C/102, and the potential difference between the points A and C is, by Ohm's law, equal to 2 x C/102=C/51. The potential difference between the points B and D is equal to Cr, where r is the unknown small resistance. Since they are equal, it follows that the value of the unknown resistance is t'i

ohm. 147. Two points, A and B, are connected by three wires, APB, AQB, ARB, whose resistances are 1, 2, and 3 ohms respectively, and A is also joined to R, the middle point of ARB, by a wire ASR of 2 ohms resistance. How much of the total current flowing from A to B passes through each of the two branches between A and R?

B. Sc. 1887

148. A battery is connected in circuit with one coil of a differential galvanometer, shunted by a wire of resistance S, and the deflection of the needle observed. The battery is then connected with both coils of the galvanometer in series, shunted by a wire of resistance 2S, and resistance is introduced into the circuit until the galvanometer indication is the same as before. Show how the internal resistance of the battery may be obtained from these two observations. B. Sc. Honours 1885. The proportion of the total current which passes through

the shunted galvanometer is the same- -S/(G x S)--in both cases,

if the resistance of the two coils is the same. Assuming further that with the same current the two coils produce the same effect on the needle, it follows that the current through the galvanometer in the first experiment is twice as strong as in the second. From this it can easily be proved that the internal resistance of the battery is equal to the additional resistance introduced into the circuit.

Prel. Sc. 1888.

149. What measurements would you make to test Ohm's law ? A battery of E.M.F. 10 volts is working in a circuit whose resistance is 100 ohms. How much work is done by the battery in an hour ? How is the energy required for this work produced, and what becomes of it ?

150. State Joule's law of the heat developed in wires by electric currents.

A current is passed through a coil of fine wire of 5 ohms resistance, immersed in a vessel containing 100 grammes of water, and the same current also passes through a coil of 4 ohms resistance, immersed in a vessel containing 100 grammes of alcohol. The water rises 2° while the alcohol rises 2-5° in the same time. Find the specific heat of alcohol on the assumption that the heat absorbed by the vessels may be neglected, and the current in both cases merely passes through the wire, and not through the liquids.

Vict. Int. 1885.

Prel. Sc. 1886.

151. A current passes through two wires arranged in parallel arc. The first wire is of platinum, 15 cm. long and i mm. in diameter ; the second of German-silver, 20 cm. long and 0.5 mm. in diameter. Compare the quantities of heat developed in the wires in a given time, the relative conductivities of platinum and Germansilver being 70 and 33.

152. The resistance of a copper wire, through which an electric current of unknown strength is flowing, is 3.2 ohms, and the difference of potential between its extremities is 2.5 volts. If this wire be immersed in 120 grammes of water, determine the temperature through which the water will be raised in five minutes, assuming that the water absorbs all the heat generated. [J = 41:55 x 106 ergs.]

Int. Sc. Honours 1886. [See pp. 231-233. The amount of heat generated is given by

the equation JH=E2t/R, where E=(2.5) x 108 and R=3.2 x 10°. The rise in temperature is 1°:177.]

153. The resistance of an incandescent lamp is 40 ohms, and the difference of potential between its two terminals is 45 volts. Determine the heat produced in it per hour. [Mechanical equivalent of heat=4.2 x 10'ergs.

I volt = 108 units of electromotive

force.
I ohm= 109 units of resistance.]

Int. Sc. Honours 1885. 154. A metal disc revolves in a magnetic field about an axis through its centre and perpendicular to its plane. Determine the electromotive force between centre and circumference.

Int. Sc. Honours. 1885. 155. Ninety incandescent lamps are placed in parallel circuit, and a current of 40 ampères is distributed between them, the E.M.F. between the terminals being 120 volts. The resistance of the conductors is .2 ohm, and that of the dynamo (series) is .25 ohm, and the insula

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