Question

1. In the circuit below Li mm Lz R mm mm Vyt + Volt) ^ 3 x с you are given: R= 0.2512; Li L2 1H; C = 1F and vg(t) = 5 cost. Compute the active and reactive power for each element in the circuit, and show that the powers balance out. (Note: Your tree should include the capacitor).

Do not worry about the tree part at the end of the question.

Answer 1

1 rad/sec. in. Xca 19c XL = XL2= W1, W12:11 ixu = jin m 2 j X2 =jla mm 0.252. M + Vr. 3 Ve 82 -jxc -jln Vght) = Scost = 520 be have. toop 4 Appty kit to -sto we have. the combined loop of P, and P2 Apply KVL to =0 -5 +0.252,-0.25 83 - j 183 +(j 1 - 34) 2,20. 0.25 I, - (0.25+j1) 13 = -0. 2, 0.25 +11 23 0.25 12-2, = 3ve. -32,-1,0-25) Iz & =0.75(13- &) 12 = 0.758, +0.2587 -0.7533 +0.25 23 CS scanned with CamScanner Iz = (1 +j1) 13 ☺

to outer loop we have Apply KUL so. -520° +31 ?z +(-j1) I sBy substituting equation @ -560° + j 1 Iz + (-; 1) (1 + j 1) 13 = 0. -560° + j 1 83+6 j1 + 1 ) 13 - + I 3 sco Amps from Î2 = (1 + j2) 23 I 7.071 245º. Amps. from @ 11 = (0-25+?)s slo R, 20.616 275.964° Anps. 0.25 32 current = It-&g = 20 98 20 i Amos CSScanned with CamScanner voltage =-up costao volts. --Si vols,

Pabsorbed = va coso (20)45) Coslo) Q=O. VAR's 100 watts jtu current Iz as Loo A. voltage - Izl:1) = 5248 AV P = ON 9 = 90 Pabsot bed = va cosco) Absor bed - vº sin 8 = 5*5* singo) 0 watts - 25 VAR's jXL2 Current = 12-13=5190 Noltage = - - 5 volts. (5 498) (j 1) = P=0 watts Rabsorbed 2 sxs singo) = 25 Var's -jXc 7007 1 245° A current Ia 4.071245) (12-98) 0=45-1-45°) voltage = 90 7.071 1-459 P=0 watts (70071) (7.071) sin90 Odelivered. SOVARS. 20.616 L75.964 Vect) Cuosent. (5) (20.616) cos(75.964) OREOVAR's. Pdelivered a CS Scanned with CamScaneer 25 watts.

3 VR current = 3(V2) 3(5498) z 15lao. voltage By EvL. -0 -s-vp + voltage stve - voltage = 5-tslae = stjs 7.071 <45°. S $= 45-(490) =-450 7.072x15xCos (45°) P delivered Q=0 because it is 75 watts current source. Pabsorbed Paecivered 100 watts. a absorbed Q delivered a 50 VAR'S Thank you - CSScanned with CamScanner