Question

For the circuit below, the AC voltage source has the form e = 20 V * Cos(500t + 0) (Where 20 V is the maximum Voltage) a) Find the total complex impedance of the circuit (Hint: it should have the form Z = a+bj, determine a and b) b) Now write the impedance in polar form (Hint: it should now have the form Z =Zeøj). c) Find the amplitude of the current through each component. R1 = 512 w R2 = 1012 4 mF 3 mH 20 V mm

Answer 1

Ri= 52 w 4 mf € = 20 V.285(500t ++) So, frequency of source, w=500 (a) the resistance, R & Ry R22lor are in arallel შშშ- 3mH equivalent resistance RI R2 of R 8 R2 is R= 5x16 2 33.33 Rit Ry 5+10 Now, the circuit becomes : p 20v R233.33 2 ez 4 mf J As R c & L are @ in in series combination so total impedance 200 I= 3mH is given by i = Fi Z = R + 8 (wh - we ) 33.93 +i (550*3416250 2 33 33 tj 500x 4 X163 33.33 + j (1) 2 33.33 + h = af bi So, a 2 33.33 1 eti where Z = at bj = 2 Z = a²+6² a= tan' (6) So here, Z = 1 83.33)² + 12 33.348 2 tant (3:33) - 1.7180 - 2. gggxlo Z = (1718) 33. 348 = 33.348 e 1 -2 rad 2.999x102;

( ) are in series current amplitude As all the components combination so the through each component will be given by Maximum will be same and 1. z Voltage 17 l implies Izl only value 20 2 Z of Zzz. •phase (4) does not matter for amplitude 20 А 33.33 Io = 600.00 6 X10S A = 600.006 mA