A 29.0 mH inductor has a reactance of 1.50 k.(a) What is the frequency of the ac current that passes through the inductor? 51000 (b) What is the capacitance of a capacitor that has the same reactance at this frequency? (c) The frequency is tripled, so that the reactances of the inductor and capacitor are no longer equal. What is the new reactance of the inductor? (d) What is the new reactance of the capacitor?
a) The reactance of an inductor is given by X w L 2 pi f L thus the frequency is f X / 2 pi L 1500/(2*pi*29E-3) 8232 Hz b) The reactance of a capacitor is X 1 / 2 pi w C solving for C we get C 1 / (2*pi*X) 1 / (2*pi()*8232*1500) 1.28891E-08 F c) and d) use the expressions above to calculate the new reactances replacing w with 3*w.
XL Omega x L 2 x Pi x f x L 2 x Pi x 10 000 x zero.015 300 x Pi 942 [Ohms], roughly. (Pi is reasonably higher than three.14 so the unique worth could be somewhat more, however the influence is distinctive ample for engineering functions, being good inside 1%.)
