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In general it will be found that on thus making contact the galvanometer needle is suddenly deflected. We shall shew, however, that if the condition C1R, C, R2 hold, C1, C, being the two capacities, there will not be any current through the galvanometer, the needle will be undisturbed (see below). To compare the two capacities, then, the resistances R, K2 must be adjusted until there is no effect produced in the galvanometer, by making or breaking contact, and when this is the case we have

C1/C2 = R2/R1,

and R1, R, being known, we obtain the ratio c1/C2. In performing the experiment it is best to choose some large integral value, say 2000 ohms for R1, and adjust R, only. We proceed to establish the formula

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No current will flow from A, to A, if the potential of these two points be always the same. Let v。 be the constant potential of the pole of the battery in contact with B1 and B2, V1 that of the other pole. Let v be the common potential of A, and A, at any moment during the charging, and consider the electricity which flows into the two condensers during a very short interval 7. The poten

tial at c is v1, and at A, and A, it is v at the beginning of the interval. The current along C A, will be then (V1 —V)/R1, and along C A2, (V1-V)/R2; and if the time be sufficiently small, the quantity which flows into the two condensers will be respectively (v, -V) T/R, and (v,-v) T/R2 inflow of this electricity will produce an increase in the potential of the plates A, and A2; and since, if one plate of a condenser be at a constant potential, the change in the potential of the other plate is equal to the increase of the charge divided by the capacity, we have for the increase of the potential at A, and A, during the interval 7, when T is very small, the expressions (V1-v) 7/C, R, and (v1-V) T/C2 R2 respectively.

Q Q

By the hypothesis A, and A, are at the same potential at the beginning of the interval T, if the two expressions just found for the increment of the two potentials be equal, then the plates will be at the same potential throughout the interval.

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Thus, if c1 R1 = C2 R2 the plates A, A, will always be at the same potential, and in consequence no effect will be produced on the galvanometer.

The complete discussion of the problem ('Philosophical Magazine,' May 1881) shews that the total quantity of electricity which flows through the galvanometer during the charging is

(V1 —v。) (R1 C1 —R2 C2) / (G+R1 +R2)

where G is the resistance of the galvanometer. It follows also that the error in the result, when using a given galvanometer, will be least when the resistances R, and R2 are as large as possible; and that if we have a galvanometer with a given channel, and wish to fill the channel with wire so that the galvanometer may be most sensitive, we should make G = R1 + R2.

The effects of electric absorption sometimes produce difficulty when great accuracy is being aimed at. They may be partially avoided by making contact only for a very short interval of time. For a fuller discussion of the sources of error reference may be made to the paper mentioned above.

Experiments.--Compare the capacities of the two condensers, (1) approximately; (2) by the null method last described.

Enter results thus :

Condensers A and B.

(1) 8, (mean of 3 observations) 223 scale divisions.
8, (mean of 6 observations) 156
8 (mean of 3 observations) 225,

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82. Measurement of the Capacity of a Condenser.

The methods just described enable us to compare the capacities of two condensers-that is, to determine the capacity of one in terms of that of a standard; just as Poggendorff's method (§ 80) enables us to determine the E.M.F. of a battery in terms of that of a standard. We have seen, however, in section 74 how to express in absolute measure the E.M.F. between two points; we proceed to describe how to express in absolute measure the capacity of a condenser.

Charge the condenser with a battery of E. M.F., E through a galvanometer, and let ẞ be the throw of the needle, k the reduction factor of the galvanometer, T the time of swing, A the logarithmic decrement, c the capacity of the condenser, and Q the quantity in the charge.

Then

Q k T (1 + λ) sin ß

C= =
E

ПЕ

by formula (4) of p. 585.

Shunt the galvanometer with 1/(n-1)th of its own resistance G, so that 1/nth only of the current passes through the galvanometer; let B be the resistance of the battery; pass a current from the battery through a large resistance R and

the galvanometer thus shunted, and let i be the current, the deflexion observed. Then we have

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for 1/nth of the current only traverses the galanometer, and produces the deflexion ;

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The quantities on the right-hand side of this equation can all be observed, and we have thus enough data to find c.

To express c in absolute measure R, B, and G must be expressed in absolute units.

In practice B will be small compared with R, and may generally be neglected; n will be large, probably 100, so that an approximate knowledge of G will suffice. T may be observed, if it be sufficiently large, by the method of

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simply by noting the time of a large number of oscillations.

The method assumes that the value of E is the same in the two parts of the experiment. A constant battery should therefore be used, and the ap

paratus should be arranged so that a series of alternate observations of ẞ and 0 may be rapidly taken. Fig. 80 shews how this may be attained. One plate B of the condenser is

connected to one pole of the battery and to the galvanometer; the other plate A is connected to the electrode F of the Morse key. The other pole of the galvanometer is connected to the electrode E, so that in the normal position of the key the two plates are in connection through the galvanometer and the key E F.

The second pole of the battery is connected to one electrode K of a switch, and the electrode D of the Morse key is connected with another electrode K, of the switch. The centre electrode E of the key is connected through the resistance R to the third electrode K, of the switch. s is the shunt. With the switch in one position contact is made between K and K, ; on depressing the key the condenser is charged, the galvanometer being out of circuit, and on releasing the key the condenser is discharged through the galvanometer. Note the zero point and the extremity of the throw, and thus obtain a value 8 for the throw, in scale divisions.

Shunt the galvanometer, and move the switch connection across to K2. A steady current runs through the resistance R and the shunted galvanometer; let the deflexion in scale divisions be d; reverse the connections, and repeat the observations several times. The damping apparatus described in the previous section will be found of use. By measuring approximately the distance D between the scale. and needle we can find tan 0 and sin ẞ in terms of d and 8. An approximate value only is required of D.

Experiment. - Determine absolutely the capacity of the given condenser.

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