Question

2.15. Convert the circui indicated. ts as Electrical Circuit Concepts 101 (a) Use Z for all elements. a a o 9Ω bo (b) Use Y for all elements. a a o

Answer 1

@) Both ar and jobs are in Series į » Lucem ۱ Combination is z = 9+3162, Convension: R and jxq are in Combination is z = R(5x) parallel z = &R R + IX, :: R65x) = 9+flor Rt'ix, Multiply and divide LHS with (R="x) Reixu), Ge-jx.) х (P +5x2) CR-jx, j = 9+316 ; R² x - j² px? R2-548 +iXR -? x{ **** = 9+16 g 2² x + R2 = 9+5lb (332-1) - R² + x² Equating real and we set imaginary terms on both sides

22+ > R²+x? 7 R²+x2 = 5 - 12 pot = 16 R²+x22 Equating o and ③ we get XY - GDR X = 0.5638 Substitusing X value in equation we get R2+0.56387 | (0.5638) 1.31792 0.31+g3 ? - R = 9+1,317 la IR=37.39 ) I 0.317 Substituting Rin equation ③ we get X1 = 0.563 (37.391) >> X = 21.05ın 537.391 3521.051

o > &as islas as and jibs are in Paraines, Combination is Y - 9+s. - Y b- Conversion: G and i Be are in Combination is Series, Y= G("Be) - It Be Glo Bc) - atill Gribe Multiply and divide las with (GajBc ) GCBc), G-Be), a több = 9+ 16 Gti Be * (Große) = 5 GF Bc - 3²GB G-18G +isa-j? R? jG² Bc + G82 22 + 2 = 9tl Equating real and imaginary GEBc (-:;?_-1) terms on bom sides we set G²+88 = 16 ) G²+B2 = G Bcn - >

Equating equations 1 and ② we set by cope > Be - Gala > 0 · Be = 0.563 G Substituting Be in equation is we get G+(0.56365. G(0.5636) 1.3170 = 0.563 G Ga 1649,394 =>G= 34.428 5) - 0.563 get Substituting Gin equation ③ we B = 0.563(37.428) s I Be = 21.07251 G 327,4285 21.0725