Given are following details,
Resistance /phase( R ) = 10 Ω . (R) =10\varOmega. ( R ) = 10 Ω .
Inductance /phase( L ) = 42 m H (L) = 42mH ( L ) = 42 m H
Hence Inductive reactance( X L ) = L ω = 42 × 1 0 − 3 × 2 π × 50 = 13.19 Ω . (X_L) =L\omega=42\times10^{-3}\times2\pi\times50=13.19\varOmega. ( X L ) = L ω = 42 × 1 0 − 3 × 2 π × 50 = 13.19 Ω .
a) The perphase impedance( Z ) = R + j X L = 10 + j 13.19 Ω (Z) =R+jX_L=10+j13.19\space\varOmega ( Z ) = R + j X L = 10 + j 13.19 Ω
b) Line voltage( V L ) = 415 V (V_L) =415V ( V L ) = 415 V (given in question)
c) Phase voltage ( V P ) = V L 3 = 415 3 = 239.6 V (V_P) =\frac{V_L}{\sqrt3}=\frac{415}{\sqrt3}=239.6 V ( V P ) = 3 V L = 3 415 = 239.6 V
d) Phase current( I P ) = V P Z = 239.6 10 + j 13.19 = 14.17 ∠ − 52.83. A (I_P) =\frac{V_P}{Z}=\frac{239.6}{10+j13.19}=14.17\angle-52.83. A ( I P ) = Z V P = 10 + j 13.19 239.6 = 14.17∠ − 52.83. A
Powerfactor = cos ( 52.83 ) = 0.604 =\cos(52.83) =0.604 = cos ( 52.83 ) = 0.604
e) Overall power dissipated in the 3phase system = 3 × I P 2 × R = 3 × 14.4 7 2 × 10 = 6281.43 W =3\times I_P^2 \times R=3\times14.47^2\times10=6281.43W = 3 × I P 2 × R = 3 × 14.4 7 2 × 10 = 6281.43 W
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