Two coil are connected in series across a 200v 50 ac supply. The powers input to the circuit is 2 kw ad 1.15 KVAR. If the resistance and the reactance of first coil are 5Ω and 8Ω respectively, calculate the resistance and reactance of the second coil. Calculate the active power and the reactive power for both the coils individually. -

Mumbai University > FE > Sem 1 > Basic Electrical and Electronics Engineering

Marks: 8 M

Year: Dec 2014

r1=5Ω, X1=8Ω

PACTIVE=2000W

PREACTIVE=1150VAR

$P_{APPARENT}$ $=\sqrt{(2000)^2+(1150)^2} \\ =2307.054 VA$

$\cos \emptyset=\dfrac{P_{ACTIVE}}{P_{APPARENT}}=0.8669 \\ P_{APPARENT}=VI \\ I=\dfrac{2307.054}{200} \\ =11.5353 A \\ Z=\dfrac{V}{I}=\dfrac{200}{11.5353}=17.3381 \Omega\\ \cos \emptyset=\dfrac{r_1+r_2}{Z} \\ r_2=Z \cos \emptyset-r_1 \\ r_2=10.0304 \Omega \\ P_{reactive}=I^2(X_1+X_2) \\ X_2=\dfrac{P_{REACTIVE}}{I_2}-x_1 \\ =8.6425-8 \\ X_2=0.6425 \Omega$

For coil 1

$\bar{Z_1}=5+j8 \\ =9.434 \angle 54.995^0 \Omega \\ V_1=108.824\angle 57.995^0$

PREACTIVE 1 $=V1 I \sin 57.995 \\ =1.064 KVAR$

PACTIVE 1 $=V1 I X \cos 57.995 \\ =665.309 W$

For coil 2

$\bar{Z_2}$ $=10.0304+j0.6425 \\ =10.0509 \angle 3.665^0$

$V_2= 115.941 \angle3.65 \\ P_{REACTIVE 2}=V-2 \sin 3.665=85.491 VAR \\ P_{ACTIVE 2}=V_2 \cos 3.665=1334.679W$