Question

An inductor of 247 mH with a resistance of 37 Ω is connected to a power supply with a maximum voltage of 336 V and a frequency of 71 Hz. Find the current in the circuit. Answer in units of A. 022 (part 2 of 3) 10.0 points Find the phase angle between the current and applied voltage. Answer in units of ◦ . 023 (part 3 of 3) 10.0 points Find the power loss in the inductor. Answer in units of W.

Answer 1

(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

Step-by-step 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;

`V_(rms) = 0.7071V_o\\\\V_(rms) = 0.7071 \ * \ 336\\\\V_(rms) = 237.586 \ V\\`

The inductive reactance is given as;

`X_l = \omega \ L\\\\X_l = 2\pi f L\\\\X_l = 2\pi (71)(247 * 10^(-3))\\\\X_l = 110.202 \ ohms`

The impedance of the A.C circuit is given as;

`Z = √(X_l^2 + R^2) \\\\Z = √((110.202)^2 + (37)^2)\\\\Z = 116.248 \ ohms`

(i) The current in the circuit is given as;

`I_(rms) = (V_(rms))/(Z)\\\\ I_(rms) =(237.586)/(116.248) \\\\I_(rms) =2.044 \ A`

(ii) the phase angle is given as;

`tan \phi = (X_l)/(R)\\\\tan \phi =(110.202)/(37) \\\\ tan \phi =2.9784\\\\\phi = tan^(-1) (2.9784)\\\\\phi = 71.441 ^0 \\\\`

(iii) The power loss in the inductor is given as;

P = IVcosΦ

P = (2.044)(237.586)Cos(71.441⁰)

P = 154.58 W