Electronic apparatus for biological research electronicappara00dona Year: 1958 INDUCTANCES, CAPACITANCES AND RESISTANCES on 7 by 90 degrees, and Vq lags on / by 90 degrees. It follows that Vj^ and Vq are in anti-phase with one another, that is, they pass though maxima and minima in step with each other, but with opposite polarity, as suggested in Figure I slnQjt Figure The instantaneous potential difference between A and B is y^ minus Vq, and the modulus of the reactance of the combination is \vi^ — vdJI which equals \vi\ll — \vq\II. However \vjjll = Xj^ and \vq\II ^= Xq so the r
Electronic apparatus for biological research electronicappara00dona Year: 1958 INDUCTANCES, CAPACITANCES AND RESISTANCES on 7 by 90 degrees, and Vq lags on / by 90 degrees. It follows that Vj^ and Vq are in anti-phase with one another, that is, they pass though maxima and minima in step with each other, but with opposite polarity, as suggested in Figure I slnQjt Figure The instantaneous potential difference between A and B is y^ minus Vq, and the modulus of the reactance of the combination is \vi^ — vdJI which equals \vi\ll — \vq\II. However \vjjll = Xj^ and \vq\II ^= Xq so the reactance is Xj^ — Xq. This is the reason for taking capacitive reactance as negative and inductive reactance as positive. Common sense suggests that if a number of reactances are connected in series, the effective reactance ought to be obtained by adding them all up. And so it can be, for The impedance of the arrangement between C and D is therefore R+J() = ' +i(''^ - ^) When ft) is small, coL is smaller than l/a>C and the circuit behaves as if it contained only the resistance and a capacitance C'such that XjcoC = l/o^C — oiL. When ft> is large, mL is larger than IfoiC and the circuit behaves as if it contained only the resistance and the inductance L' such that coL' = coL — l/ft)C. When oy has the critical value \l(LCy- the reactances cancel, and it is as if only the resistance was there. This is the basis of series resonance. P Vv^A/ 1 0 Figure Series resonance If series L, C, and R are connected to a constant voltage alternator (Figure ), the current is given by E 1 = ''+jh-^) 74
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