RLC Resonant Circuits - University of Cambridge

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RLC Resonant CircuitsAndrew McHutchonApril 20, 20131 Capacitors and InductorsThere is a lot of inconsistency when it comes to dealing with reactances of complex components. The formatfollowed in this document is as follows. Theimpedance,Z, of a component or a circuit is defined as,Z=R+j X(1)whereRis the resistance,jis the imaginary unit, andXis the reactance. Note that the imaginary unit isoutsidethe reactance and there is a plus sign betweenRandj and inductors are both components which can store energy: capacitors store it in an electric field andinductors in a magnetic field. Ideal capacitors and inductors are assumed to have zero resistance and so have apurely imaginary impedance,ZC=1j C= j CZL=j L(2)Following the convention in equation 1 we define the reactances to be,XC= 1 CXL= L(3)note that the minus sign is includedinsideXC, this is to ensure we get a plus sign in equation 1. You will oftensee capacitive reactance being quoted without this minus sign - be very careful!

1 Capacitors and Inductors There is a lot of inconsistency when it comes to dealing with reactances of complex components. The format followed in this document is as follows. The impedance, Z, of a component or a circuit is de ned as, Z = R + jX (1) where Ris the resistance, jis the imaginary unit, and Xis the reactance.

  Inductors