Admin: • Assignment 6 is complete. • Assignment 7 is posted • Due Monday (20th) . • Proposed second mid-term date: • Wednesday May 6th • Any conflicts? • Final is Friday May 22nd, 10:30am - 12:30am SHL 130 • Office hours cancelled today – ask me questions after class, or by email. Capacitors in AC circuits No charge flows through a capacitor A capacitor in a DC circuit acts like a break (an open circuit) But in AC circuits charge build-up and discharge mimics a current. •The consequences of this are peculiar! • Voltage and current are not in phase: • Current leads voltage by 90 degrees • Impedance of Capacitor decreases with increasing frequency Capacitative reactance – use this for calculations which are independent of phase: 1 XC = wC Capacitative impedance. Complex form – use where phase dependance is important: ZC = 1 jwC 30-7 AC Circuits with AC Source Example 30-10: Capacitor reactance. What is the rms current in the circuit shown if C = 1.0 μF and Vrms = 120 V? Calculate (a) for f = 60 Hz and then (b) for f = 6.0 x 105 Hz. XC = 1 wC Note: we can simply use reactance (XC) if dealing with phase independent quantities like rms. But the answer is not valid at any given instant in time: for that we need the impedance (ZC) Copyright © 2009 Pearson Education, Inc. Inductors in AC circuits Inductive Load vS = Asin w t vL = L diL dt Asin w t = L diL dt A A sin w t dt = cosw t ò L wL A A iL = sin(w t - 90) = cos(w t -180) wL wL VL ( jw ) = AÐ(w t - 90) ”inductive reactance” A XL=ωL I L ( jw ) = Ð(w t -180) wL V ( jw ) ZL = L = w LÐ90 I L ( jw ) cos(90) j sin(90) j Z L = jw L ”inductive impedance” iL = • Voltage and current not in phase: • Current lags voltage by 90 degrees • Impedance of Inductor increases with increasing frequency Play animation 30-7 AC Circuits with AC Source Example 30-9: Reactance of a coil. A coil has a resistance R = 1.00 Ω and an inductance of 0.300 H. Determine the current in the coil if (a)120-V dc is applied to it, and (b) 120-V ac (rms) at 60.0 Hz is applied. XL=ωL Note: we can simply use reactance (XL) if dealing with phase independent quantities like rms. But the answer is not valid at any given instant in time: for that, we need the impedance (ZL) Copyright © 2009 Pearson Education, Inc. What if there is more than one component? AC circuit analysis • Procedure to solve a problem – – – – Identify the source sinusoid and note the frequency Convert the source(s) to complex/phasor form Represent each circuit element by it's AC impedance Solve the resulting phasor circuit using standard circuit solving tools (equivalent impedances, voltage/ current divider, KVL,KCL,Mesh, Thevenin etc.) – Find the real part of the solution, and write is as a function of time.