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in Physics by (63.5k points)

An impedance (6 + j 8) is connected across 200-V, 50-Hz mains in parallel with another circuit having an impedance of (8 − j6) Ω. Calculate (a) the admittance, the conductance, the susceptance of the combined circuit (b) the total current taken from the mains and its p.f

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Y1 = 1/(6 + j8) = (6 - j8)/(62 + 82) + 0.06 - j0.08 Siemens, 

Y = 1/(8 - j6) = (8 + j6)/100 = 0.08 + j0.06 Siemens

(a) Combined admittance is 

Y = Y1 + Y2 = 0.14 −j0.02 = 0.1414 ∠− 88º′ Siemens 

Conductance, G = 0.14 Siemens ; Susceptance, B = −0.02 Siemens (inductive) 

(b) Let V = 200 ∠ 0º ; I = VY = 200 × 0.1414 ∠−8º8′ V = 28.3 ∠−8º8′ 

p.f. = cos 8º8′ = 0.99 (lag)

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