Question

A voltage V= 150+j180 V is applied across an impedance and current flowing is found to be 5-j4 A. Calculate followings: i) Scalar Impedance ii) Resistance iii) Reactance iv) Power Consumed Also sketch phasor diagram of voltage and current.

Answer 1

Given : voltage V = 150 + j 180

I =5 - j 4.

To find : (i) scalar impedance (ii) resistance (iii) reactance

Solution :

V = I Z

Z = V/I

=> Z   =  (150 +  j 180  )/(5 - j 4)

=  (150 +  j 180  )(5 + j 4) / (5 - j 4)(5 + j 4)

= {750 - 720 + j(900 + 600)} / (25 + 16)

= (1470 + j 1500)/49

Scaler impedance  =  √(1470)² + (1500)² / 49  = 2100/49 = 42.86 Ω

Resistance = 1470/49  = 30 Ω

Reactance = 30.61  Ω

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Answer 2

$\huge\star\underline{\mathtt\red{so}\mathtt\green{l}\mathtt\blue{ut}\mathtt\purple{i}\mathtt\orange{o}\mathtt\pink{n}}\star\:$

V = I Z

Z = V/I

=> Z   =  (150 +  j 180  )/(5 - j 4)

=  (150 +  j 180  )(5 + j 4) / (5 - j 4)(5 + j 4)

= {750 - 720 + j(900 + 600)} / (25 + 16)

= (1470 + j 1500)/49

Scaler impedance  =  √(1470)² + (1500)² / 49  = 2100/49 = 42.86 Ω

Resistance = 1470/49  = 30 Ω

$\colorbox{pink}{Reactance = 30.61}$

$\sf\red{hope \: this \: helps \: you!! \: }$