EE201 Lecture 33 P 1 Phasors cont Example Find the Thevenin equivalent for the circuit shown below 2 vs t 10cos t A 1H B 2F voc 0 5voc Step 1 Compute Voc using phasor methods Vs 10 0 Using nodal analysis at A VA 10 1 0 5 Voc VA Voc 0 1 2 j Because IL YL j VL 1 j L VA Voc EE201 Lecture 33 P 2 Grouping like terms in Eq 1 0 5 j VA 0 5 j Voc 5 2 nodal analysis at B 1 j Voc VA j 2 Voc 0 Because Ic Yc j Vc j C Voc j Voc j VA j2 Voc 0 VA Voc Putting Eq 3 into Eq 2 3 j2 Voc 5 Voc j2 5 2 5 90 voc 2 5 cos t 90 V 2 5 sin t V EE201 Step 2 Find Isc 2 10cos t Lecture 33 P 3 1H 2F Voc 0 5voc Since voc 0 dependent current source is deactivated and acts as an open circuit element The capacitor is by passed by the short between Equivalent impedance for resistor and inductor in series Zeq R j L 2 j 5 26 6 Isc EE201 Isc Lecture 33 10 0 P 4 4 47 26 6 5 26 6 isc t 4 47 cos t 26 6 Step 3 Find ZTH and draw Thevenin equivalent ZTH Voc Isc 2 5 90 4 47 26 6 0 56 63 4 ZTH 0 56 cos 63 4 j sin 63 4 ZTH 0 25 j0 5 EE201 Lecture 33 P 5 0 25 0 25 j0 5 2 5 sin t 2F 2 5 sin t Example Find the value of L so that the current is in phase with the source voltage R vs t 10cos t is t L C EE201 Lecture 33 P 6 Step1 Evaluate equivalent impedance 1 Zeq j R j L j C Zeq j R j L 1 C Step 2 Relate current and voltage Zeq j Vs Is 10 Is There can be no imaginary component in Zeq j L 1 C 0 1 L 2 C EE201 Lecture 33 P 7 Example Find vs t Is t 2cos 500t 133mH vS 100 13 3 F Step 1 Find equivalent impedance admittance 1 Yeq j R Yeq j 1 100 1 j C j L 1 j 500x13 3x10 j 6 500x13 3x10 3 Yeq j 0 01 j6 65x10 3 j 1 5x10 2 EE201 Lecture 33 Yeq j 0 01 j8 39x10 3 0 013 40 Zeq j 1 Yeq j 76 9 40 Step 2 Compute vS t using phasors is t Is 2 0 Vs Zeq j Is Vs 153 8 40 or explicitly in time vS t 153 8 cos 500t 40 P 8
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