Finding Frequency of 20mH Inductor & 30 Ohm Resistor in Parallel

[mugzieee]

im given a a 20-mH inductor and a 30 ohm resistor in parallel. Z_in is 25 degrees. and I am asked to find the frequency omega in rad/s here's what i try to do:
25=(jw.02*30)/(jw.02+30), and solve for w, but i don't get the right answer.
what is it that I am doing wrong?

 

[Curious3141]

im given a a 20-mH inductor and a 30 ohm resistor in parallel. Z_in is 25 degrees. and I am asked to find the frequency omega in rad/s here's what i try to do:
25=(jw.02*30)/(jw.02+30), and solve for w, but i don't get the right answer.
what is it that I am doing wrong?

You're given the phase shift (in degrees). Remember that the phase shift is the argument of the complex impedance of the combination.

So you started out determining the impedance correctly :

$$Z = Z_L // R = \frac{j\omega L}{R + j\omega L}$$

but you then equated that to 25 degrees, which makes no sense. Keep in mind that Z is a full complex number with a magnitude and an argument. You should rearrange Z to the form $$Z = re^{j\theta}$$ where $$\theta$$ is the radian equivalent of 25 degrees (25/180*pi) Find an expression for the argument in terms of the arctangent of a ratio between the resistance and the inductance times omega. That's the equation you need to solve for omega.

The first thing you should do in that expression for Z is to make the denominator real.