Answer:
(i) The current in the circuit is 2.044 A
(ii) the phase angle is 71.441⁰
(iii) The power loss in the inductor is 154.58 W
Explanation:
Given;
inductance, L = 247 mH
resistance, R = 37 Ω
maximum voltage, V₀ = 336 V
frequency, f = 71 Hz
The rms voltage is given as;
[tex]V_{rms} = 0.7071V_o\\\\V_{rms} = 0.7071 \ \times \ 336\\\\V_{rms} = 237.586 \ V\\[/tex]
The inductive reactance is given as;
[tex]X_l = \omega \ L\\\\X_l = 2\pi f L\\\\X_l = 2\pi (71)(247 \times 10^{-3})\\\\X_l = 110.202 \ ohms[/tex]
The impedance of the A.C circuit is given as;
[tex]Z = \sqrt{X_l^2 + R^2} \\\\Z = \sqrt{(110.202)^2 + (37)^2}\\\\Z = 116.248 \ ohms[/tex]
(i) The current in the circuit is given as;
[tex]I_{rms} = \frac{V_{rms}}{Z}\\\\ I_{rms} =\frac{237.586}{116.248} \\\\I_{rms} =2.044 \ A[/tex]
(ii) the phase angle is given as;
[tex]tan \phi = \frac{X_l}{R}\\\\tan \phi =\frac{110.202}{37} \\\\ tan \phi =2.9784\\\\\phi = tan^{-1} (2.9784)\\\\\phi = 71.441 ^0 \\\\[/tex]
(iii) The power loss in the inductor is given as;
P = IVcosΦ
P = (2.044)(237.586)Cos(71.441⁰)
P = 154.58 W
