in which r = Resistance of the a.c. milliammeter in ohms R = Resistance of the shunt resistor in ohms -X"c = The reactance of the capacitor to be measured in ohms
Z=The impedance of the circuit combination, in ohms. The Xc values as used in formula (3) are the effective resistance values of capacitors given by formula (1).
From the above mathematical relationship, curves may be plotted as shown in chart, fig. 3. In this chart the resistance value from 500 to 5,000 ohms and capacitors from 0.1 to 15 microfarads aré covered. The chart is used as follows:
The value of r, is the resistance of the meter being used.
The value of R is obtained by an ohmmeter (d.c.). The a.c. (nilliammeter reading is obtained by placing it across the points A and B of fig. 2 as indicated.
The intersection of the line corresponding to the a.c. milliam-meter readings and the resistance given by the ohmmeter will intersect on one of the curves and following this curve out, the value of the condenser in microfarad is obtained.
Example.—If the a.c. milliammeter reads 30 M.A., and the resistance (R) is found by the ohmmeter to be 2,500 ohms, what is the value of the condenser?
Solution.—Following the curve fig. 3 at the intersection of the 30 M.A. and the 2,500 ohms line shows the value of C to be 1.82 microfarads.
Inductive Measurements.—Inductance values may be obtained in a manner similar to that already described in capacity measurements. It should however be remembered that inductive reactance is vectorially positive whereas capacitive reactance is negative, and that the larger the value of the inductive reactance the lower will be the reading of the a.c. milliammeter. Also the larger the capacitive reactance the higher will be the reading of the a.c. milliammeter.
The formula for the inductive reactance (X J in ohms is:
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