Current Magnitude in Series RL Circuit

[Cast_Member]

Hi,

I some have problems regarding the series RL circuit again and this time, it is the magnitude of the current. I have tried to apply the solution that was given to me in the text book. Here is my attempt on the question:

"R=71 Ohms, L=39 mH & e is a 34 kV, 310Hz power supply. What is the magnitude of the current?"

The solution:

6.28x310Hzx39mH=759

759/71tan=84.7 degrees

71^2+84.7^2 square root=110.52

34/110.52=307

I don't really know what I'm doing. Thanks.

 

[Diver300]

You don't need to worry about phase angles for this, and you just about never square an angle.

You've worked out ωL in the right way, but the inductor's impedance at 75.96 ohms. (I guess that you didn't put 39 mΩ as 0.039 Ω) That's about the same as the resistance so we are looking at somewhere around 1½ times that, about of 100 Ω

But to work it out correctly,

impedance = √(R²+(ωL)²) = √(71²+75.96²) = 103.98 Ω
(Looks right, about 100 Ω)

so the current is 34000/103.98 = 327.0 Amps

If you did want to work it out with angles, the phase angle is atan (75.96/71) = 46.993 degrees

Then your impedance is either

75.96 / sin (46.993) or 71 / cos (46.993), both of which come out to be 103.98 Ω

(I am so glad this is homework and not a backyard generator project. There are all sorts of warnings that go with 3 MVA systems!)

 

[Ratchit]

Cast_Member,

I don't really know what I'm doing. Thanks.

That's correct.

I = V/Z so,

Z = R+j(Xl)

Xl = j(2*3.14*310*39E-3)=75.98/_90°

Z = 71/_0°+75.98/_90°=103.99/_46.94°

I = 34E3/Z = 34E3/(103.99/_46.94°) = 326.95/_-46.94° amps

Ratch

 

[RCinFLA]

Little trick that can help save time on tests.

Make sure you have a calculator with Polar to Rectangular and Rectangular to Polar conversion.

Do complex number addition and substraction in Rectangular coordinates. Do Multiplication and division in Polar coordinates.

With this there is some quick tricks to convert series RL or RC to parallel equivalents or parallel RL or RC to series equivalents. After you do it for a while your fingers do the job without even thinking about it.

 

[Cast_Member]

Thanks everyone.