Question

For the circiut shown a) Find the load impedance 21 For mximum power to the load b) Find the maximum power to the load XA R: 33

Answer 1

Maximum Power Transfer Theorem for AC Circuits

It can be stated as in an active network, the maximum power is transferred to the load when the load impedance is equal to the complex conjugate of an equivalent impedance of a given network as viewed from the load terminals.

Based on requirement , we use polar form to rectangular form and vice versa.

To find the maximum Power transfered to the load, we need to find the renine suivalent circuit. Given circuit 18. 4:41 - 406A +X62 Dz. 312 Note that, Reactance must be the quaginary. So, anductance is positive nce and capacitive as negative reactance. Now, find the venins equivalent circuit, . Accoeling to the soun's Statement a ve thevenins voltage (VT) Source is an sesies with the equivalent resistance (RAH) Find Rth (08) 7th - Remove the - Shilt the voltage Source and open the current source, So, the circuit 96. | X - 34 - :-RTH = (3+34) || (-16) 323 RTA = (3+34) * (-36) - 3+34-96 BTH = -189 -61)24 - 24-189 = (8.3 -0.463) 2 en rectangular - 3-92 3-82 form a) (08) ITH = 8.32 -3-16 Rn polas form → Accading to the Statement of maximum Power transfer theolenna load impedance (4) is the complex conjugate of ETH -:72 - THE = (8-3-0.48)*sx (8.3+0.463)2 mone 1:10 Gight

--Port Villa Pomove the Man Who (92 cmt % 300 1010^ 3n Ville V. Vill in VO .nl mode 1, fiyating akate - voltage avalycis -> wy - 400 -> (3] = 40 - (0.34 +0.254) v, -(0.2sí) Vy = 40 --> 0 At nodea. -- (-0.25;) V+ V) (3, 30) - 0 -) (-0.25 j) v, + (0.848), = 0 -> by solving equations ① and ③ we get . Vi -(92.87-44.963) V -(104-53727.314 ) v ant V2 = (27.64 -14.2-13) V . (31.11 -23:1.3111 ) v .:: VH = Vy: (12:4.641 - 14-213) v Co, thevening equivalent circuit 98 2.71168.3.00463) 14:(01.00 - 14-093)v

Now, the circuit is, -I = (8.3-0.4.63). 67.64-14-213) Vit 172 = -- (8-340-46j). find max Power 1) Now, we have transfered to the load , 82 VTH (27664-14-2-13)2 8(8.3 +0.469) 4 (560-asli - 187 1963) (66-456+3.683) Pinay = (7.449 - 12-304]) waths an rectangular (05) I loom Pmax = 14.5412 (57.48 watts an polar form.