THE ELECTRIC CURRENT

Excerpts

• THE ELECTRIC CURRENT

  This operation, in which a compound body is decomposed by an electric current, is called Electrolysis, and the mode in which the current is transmitted is called Electrolytic Conduction.

• THE ELECTRIC CURRENT

  There will thus be a transference of positive electricity from A to B along the path travelled over by the pith ball, and this is what occurs in every electric current, namely, the passage of electricity along a definite direction.

• THE ELECTRIC CURRENT

  The ratio of the numerical value of the electromotive force to that of the current is called the Resistance of the conductor.

• THE ELECTRIC CURRENT

  The whole work done by the external electromotive force in urging electricity through the body is therefore spent in generating heat.

• THE ELECTRIC CURRENT

  According to the theory of molecular motion of which he has himself been the chief founder, every molecule of the fluid is moving in an exceedingly irregular manner, being driven first one way and then another by the impacts of other molecules which are also in a state of agitation.

• THE ELECTRIC CURRENT

  This analogy is so complete that we may make use of the same terms in describing the behaviour of media under the action of electromotive force as we apply to bodies under the action of stress.

• THE ELECTRIC CURRENT

  The excess of water in the tube D may be taken to represent a positive charge of electricity on one side of the dielectric, and the excess of mercury in the tube A may represent the negative charge on the other side.

• THE ELECTRIC CURRENT

  The electric strength of a dielectric medium depends on the nature of the medium and its density and temperature.

• THE ELECTRIC CURRENT

  The light of the spark or other discharge is made to fall on the slit of the collimator of the spectroscope, and after being analysed by the prisms is observed through the telescope.

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  But there are methods by which the difference of potential of the conductors may be maintained constant, in which case the current will continue to flow with uniform strength as a Steady Current.

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  Thus we see that the electric current has a magnetic action which is exerted outside the current, and by which its existence can be ascertained and its intensity measured without breaking the circuit or introducing anything into the current itself.

• THE ELECTRIC CURRENT

  The galvanometer is the most convenient instrument for measuring the strength of electric currents. We shall therefore assume the possibility of constructing such an instrument in studying the laws of these currents, and when we say that an electric current is of a certain strength we suppose that the measurement is effected by the galvanometer.

• THE ELECTRIC CURRENT

  The Resistance of a conductor is defined to be the ratio of the electromotive force to the strength of the current which it produces. The introduction of this term would have been of no scientific value unless Ohm had shewn, as he did experimentally, that it corresponds to a real physical quantity, that is, that it has a definite value which is altered only when the nature of the conductor is altered.

• THE ELECTRIC CURRENT

  If the wire, when the force is removed, returns to its former shape and becomes completely untwisted it is said to be elastic. Such a wire corresponds to a dielectric which acts as a perfect insulator with respect to the electromotive force employed.

• THE ELECTRIC CURRENT

  If no such permanent twist can be given to the wire by a force which is not sufficient to break it, the wire is called brittle. In like manner we may speak of those dielectrics such as air, which will not transmit electricity except by the disruptive discharge, as electrically brittle.

• THE ELECTRIC CURRENT

  In this way we may construct a mechanical illustration of the properties of a dielectric of any kind, in which the two electricities are represented by two real fluids, and the electric potential is represented by fluid pressure. Charge and discharge are represented by the motion of the piston P, and electromotive force by the resultant force on the piston.

• THE ELECTRIC CURRENT

  It would therefore seem as if a perfect vacuum would present an almost insuperable resistance to the passage of electricity. A small quantity of gas, however, introduced into the empty space renders it incapable of withstanding even a small electromotive force.

• THE ELECTRIC CURRENT

  The whole theory of the electric properties of gases is in a very imperfect state.

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  Thus there is continually kept up an influx of uncharged air to the point, a luminous discharge of electricity from the point, called the Electric Glow, and a stream of charged air in the direction of the prolongation of the axis of the cone called the Electric Wind. By checking the influx of air behind the point we may weaken the glow and by increasing the current of air by blowing we may make the glow stronger.

• THE ELECTRIC CURRENT

  We may compare this breaking down of the dielectric to what occurs when we make a little rent perpendicular to the edge of a piece of paper and then apply tension to the paper in the direction of the edge. The paper is torn through, the disruption beginning at the little rent, but diverging occasionally so as to take in weak places in the paper.

• THE ELECTRIC CURRENT

  It follows from this that neither the electric fluid, if there be such a substance, nor any ethereal medium such as is supposed to pervade all ordinary matter, is rendered luminous during the discharge, for if it were so its spectrum would be visible in all discharges.

• THE ELECTRIC CURRENT

  Hence the ball is acted on by the electric force always in the direction in which it is moving at the time, so that if it is properly suspended the electric force will not only keep up the backward and forward motion, but will communicate to the moving ball an amount of energy which it will expend in a series of rattling blows against the balls A and B.

• THE ELECTRIC CURRENT

  It is therefore quite possible that the velocity of electricity in a telegraph wire may be exceedingly small, less, say, than the hundredth of an inch in an hour, though signals, that is to say, changes in the state of the current, may be propagated along the wire many thousands of miles in a second.

• THE ELECTRIC CURRENT

  Since, therefore, we are ignorant of the true linear velocity of an electric current, we must measure the *strength* of the current by the quantity of electricity discharged through any section of the conductor in the unit of time, just as engineers measure the discharge of water and gas through pipes, not by the velocity of the water or gas, but by the quantity which passes in a minute.

• THE ELECTRIC CURRENT

  In these cases it is convenient to speak of the total current as the Electric Displacement, the word displacement indicating the final result of a motion without reference to the rate at which it takes place.

• THE ELECTRIC CURRENT

  The electromotive force, therefore, does not produce the disruptions and reunions of the molecules, but finding these disruptions and reunions already going on, it influences the motion of the constituents during their intervals of freedom.

• THE ELECTRIC CURRENT

  The best test, however, is the existence of polarization, for even when the quantity of the free ions is too small to be observed or measured, their presence may be indicated by the electromotive force which they excite.

• THE ELECTRIC CURRENT

  When the electromotive force is increasing, the increase of electric displacement is equivalent to an electric current in the same direction as the electromotive force. When the electromotive force is constant there is still displacement, but no current. When the electromotive force is diminishing, the diminution of the electric displacement is equivalent to a current in the opposite direction.

• THE ELECTRIC CURRENT

  In this way a constant circulation is kept up, each of the constituents travelling in one direction by electrolysis, and back again by diffusion, so that a permanent current may exist without any visible accumulation of the products of decomposition.

• THE ELECTRIC CURRENT

  A solution of sulphate of zinc is placed in a cell of porous earthenware, and this cell is placed in a vessel containing a saturated solution of sulphate of copper. A piece of zinc is dipped into the sulphate of zinc, and a piece of copper is dipped into the sulphate of copper. Wires are soldered to the zinc and to the copper above the surface of the liquid. This combination is called a cell or element of Daniell’s battery.

• THE ELECTRIC CURRENT

  If a man were to place his body in the line of the current so that the current from copper through the wire to zinc should flow from his head to his feet, and if he were to direct his face towards the centre of the magnet, then that end of the magnet which tends to point to the north would, when the current flows, tend to point towards the man’s right hand.

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  Or, *the resistance of a series of conductors is the sum of the resistances of the conductors taken separately*.

• THE ELECTRIC CURRENT

  Or, *the reciprocal of the resistance of a multiple conductor is the sum of the reciprocals of the component conductors*.

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  Consider next a prismatic conductor of the same material whose length is l, and whose section is unity. This is equivalent to l cubes arranged in series. The resistance of the conductor is therefore l .

Equations

• THE ELECTRIC CURRENT

  \text{Electromotive force} = \text{Current} \times \text{Resistance,}

  The electromotive force equals the current multiplied by the resistance, so the ratio of electromotive force to current is the resistance of the conductor.

• THE ELECTRIC CURRENT

  \text{Heat generated measured in dynamical units}\\ = \text{Square of Current} \times \text{Resistance} \times \text{Time.}

  The heat generated in a conductor carrying a steady current, measured in dynamical units, equals the square of the current times the resistance times the time.

• THE ELECTRIC CURRENT

  E_{12} = CR_{12}\text{,} \quad E_{23} = CR_{23}\text{,} \quad E_{34} = CR_{34}\text{.}

  Ohm's law applied to each conductor of a series, all carrying the same current C.

• THE ELECTRIC CURRENT

  E = CR \text{.}

  For the series system as a whole, the resultant electromotive force equals the current times the resultant resistance.

• THE ELECTRIC CURRENT

  E &= E_{12} + E_{23} + E_{34}\text{,}

  The resultant electromotive force of a series of conductors is the sum of the separate electromotive forces.

• THE ELECTRIC CURRENT

  R = R_{12} + R_{23} + R_{34}

  The resistance of a series of conductors is the sum of the resistances of the conductors taken separately.

• THE ELECTRIC CURRENT

  a - b = R_1C\text{,} \quad b - c = R_2C\text{,}\quad \text{and} \quad a - c = RC\text{,}

  The potential differences across the part from A to B, the part from B to C, and the whole from A to C are each the current times the corresponding resistance.

• THE ELECTRIC CURRENT

  b = \frac {R_2a + R_1c}{R}\text{,}

  The potential at an intermediate point B of a series is a weighted combination of the potentials at its ends, weighted by the resistances.

• THE ELECTRIC CURRENT

  E = C_1R_1 = C_2R_2 = C_3R_3 = CR\text{,}

  The same potential difference E between the common ends holds across each branch of a multiple arc, and across the multiple conductor as a whole.

• THE ELECTRIC CURRENT

  \frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}\text{.}

  The reciprocal of the resistance of conductors in multiple arc is the sum of the reciprocals of the component resistances; equivalently, conductivities add.

• THE ELECTRIC CURRENT

  C = C_1 + C_2 + C_3\text{,}

  The total current into a multiple arc is the sum of the currents in its branches.

• THE ELECTRIC CURRENT

  C_1 = C\frac{R}{R_1}\text{,}

  The current in any branch of a multiple conductor is the total current times the resistance of the whole divided by the resistance of that branch.

• THE ELECTRIC CURRENT

  R = \frac{l\rho}{s}\text{.}

  The resistance of a uniform conductor is its specific resistance times its length divided by its cross-section.

• THE ELECTRIC CURRENT

  R = \frac{l^2r}{m}\text{.}

  The resistance of a wire is the square of its length times its specific resistance per unit of weight, divided by its mass.

Problems

No exercises in this chapter.