Question

1Calculate the reactance of a 7 H inductor at a frequency 300 Hz? 2.If an RL circuit has a 40 Ω resistor in series with a 9 mH inductor, what will it’s impedance be at 450Hz? 3)An RL circuit has a 5 kΩ resistor and a 1.5 H inductor. At what frequency will the current lag the voltage by π/3? 4)An RL circuit has a 500 Ω resistor and a 0.1 H inductor. This circuit is driven by a 100 Hz sine wave with 2 V amplitude. What is the amplitude of the current in this circuit? Chegg expert, Please show your steps AND FORMULAS. Answer all questions

Answer 1

1) The reactance of inductor

$X_L = \omega L = 2 \pi f L = 2 \pi (300)(7) = 1.32 \times 10^4 \Omega$

2) Impeadance of the RL circuit is

$Z = \sqrt{R^2 + X_L^2} = \sqrt{R^2 + ( 2 \pi f L)^2}$

$Z = = \sqrt{(40)^2 + (2 \pi(450)(9\times 10^{-3}))^2} = 47.4 \Omega$

3) the equations for the phase angle

$\tan 60^o = \frac{\omega L}{R}$

$\tan 60^o = \frac{2 \pi f L}{R}$

$\tan 60^o = \frac{2 \pi f (1.5)}{5000}$

f = 919Hz

4) The current amplitude is

$I = \frac{E}{Z} = \frac{E}{\sqrt{R^2 + (2 \pi f L)^2}} = \frac{2}{\sqrt{(500)^2 + (2 \pi (100)(0.1))^2}} =3.97\times 10^{-3}A$