Find phasor current (impedance, etc.), need help finding polar form

1. May 8, 2013

Color_of_Cyan

1. The problem statement, all variables and given/known data

A 90Ω resistor, a 32 mH inductor, and a 5μF capacitor are connected in series across the terminals of a sinusoidal voltage source Vs = 750cos(5000t + 30)V.

Calculate the phasor current.

[Broken]

2. Relevant equations

phasor current i = V/Z

V in polar form = (Magnitude)(cos a + j sin a)

Z (inductor) = wLj

Z (capacitor) = -j/ωC

Z (resistor) = r

total impedance = Z inductor + Z capacitor + Z resistor

Conversion to other form of Z:

Z(mag) = (R2+X2)1/2

Z angle = tan-1(R/X)

from the form Z = R + jx

3. The attempt at a solution

Not sure how I would convert the voltage to polar form and then I could find the current.

But for the impedance it would be:

ω = 5000,

so, Z (inductor) = 5000*(32 x 10-3) = 160j

Z (capacitor) = -1j/(5000*(5 x 10-6)) = -40j

Z (r) = 90Ω

So Z = 90 +120jΩ

Then to polar form would be

Z(mag) = (R2+X2)1/2

Z(angle) = tan-1(R/X)

So Z(mag) = 150

Z(angle) = 36.8 deg

Z = 150 ∠ 36.8 degrees, for sure

Now for the voltage I'm not so sure, but I'm guessing the angle is just 30 so

V = 750∠30 deg

So if the voltage is correct then would the phasor current be

I = (750∠30 deg) / (150 ∠ 36.8 deg)

I = (5 ∠ -6.8 deg)A ?

Thank you.

Last edited by a moderator: May 6, 2017
2. May 9, 2013

Staff: Mentor

The polar form of your impedance is not correct. How can the magnitude be less than that of of the individual components that comprise it?

3. May 9, 2013

Color_of_Cyan

I see. I've edited the original post, so the components were supposed to be squared first then?

So what about for converting the voltage now too,

I got 150 for the impedance magnitude now.

Is the phasor current then I = 5 ∠ -6.8 deg)A now then?

Last edited: May 9, 2013
4. May 9, 2013

Staff: Mentor

The magnitude looks fine now, but your angle does not.

Be careful to place the imaginary component over the real component to form the tan of the angle for the complex number.

5. May 9, 2013

Color_of_Cyan

I keep making these silly mistakes ;/

I had the R/X switched around. It's 53.1 deg

So Z = 150 ∠ 53.1 deg then.

So is I = (5 ∠ 16.3 deg)A then? Any other mistakes I made?

6. May 9, 2013

Staff: Mentor

No, your current angle's not correct. The voltage angle is 30°, the impedance angle is 53.1°. You're calculating E/Z, so how should you handle the angles?

7. May 9, 2013

Color_of_Cyan

Would I just subtract them? 53.1 - 16.3 would be 23.1 deg then (don't know how I got 16.3, must have subtracted something wrong).

So is I is (5 ∠ 23.1 deg)A then.

I didn't know that you could just get the angle from the phase in the given voltage so that's why I asked though, thanks.

8. May 9, 2013

Staff: Mentor

You do a subtractions, yes, but the order of the operands is important. The sign of your resulting angle is incorrect because you chose to subtract the numerator's angle from the denominator's angle. This is exactly wrong When you divide in polar form, you subtract the denominator's angle from the numerator's angle.

9. May 10, 2013

Color_of_Cyan

Alright, so the phasor current I then is

( 5 ∠ -36.8 )A then, right?

Thanks for the help again.

10. May 10, 2013

Staff: Mentor

30 - 53.1 = -36.8 ???

11. May 10, 2013

Color_of_Cyan

This is so bad I keep making all those mistakes :(

I = (5 ∠ -23.1)A

12. May 10, 2013

Staff: Mentor

That result looks good.