Question

IN A SERIES R-L CIRCUIT THE INDUCTANCE20mH .THE IMPEDANCE IS 17.85.THE ANGLE OF LAGS OF THE INPUT CURRENT FROM THE APPLIED VOLTAGE BEING 63.5.FIND THE VALUE OF ANGULAR FREQUENCY AND THE RESISTANCE​

Answer 1

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Step-by-step explanation:

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Answer 2

Given: Inductance= L= 20mH

           Impedance= Z= 17.85

           Angle= Ф = 63.5°

To find: Angular Frequency (W) and The resistance(R)

Find:

Ф= tan⁻¹[ WL/R]

63.5 = tan⁻¹[ (W x 20 x 10⁻³) / R]

63.5 = tan⁻¹[ (W x 20 x ) / R x 10³]    ∵ 10³ = 1000 ; 20/1000 = 0.02

Tan 63.5 = 0.02 W / R

2= 0.02 W/ R

R = 0.02 W -------eq 1

Z = √R² =(WL)²

17.85 = √ (0.01 W)² + (W + 0.02)²

17.85 = √0.0001W² + W² + 0.0004 + 0.04W²  ∵ (a + b)² = a² +b²+2ab)

 17.85 =  0.022 W

W= 17.85 / 0.022

   = 796.875 rad/sec

R = 0.01 * W

  = 0.01 * 796.85

  = 7.98 Ω

The angular frequency is 796.875 rad/sec

The resistance is 7.98 Ω