Answer verification Series RLC, Reactance, Voltages, Current

[Ryan Walkowski]

Homework Statement

All relevant data and variables are included in the image. The questions are also included in it.

Homework Equations

My questsion is just verification. I have attempted all the asked questions on the paper. Its frustrating as the papers don't include answers to check them nor do i have access to my lecturer for another couple of days. Thus verification on what I am doing is difficult.

The Attempt at a Solution

 

[gneill]

Your current angle (polar form) is not correct. When you divide polar complex values the denominator angle is subtracted from the numerator angle.

Otherwise your methodology looks sound.

 

[Ryan Walkowski]

Are you able to tell me what the correct answer for that part is then. So i can visualise my mistake. As the way i see it is the numerator angle is 0° and the denominator angle is -2.86° those subtracted gives me an angle of -2.86° but it just dawns on me as i write this that a set of brackets might of helped me (0) - (-2.86) = 2.86° Thats pretty basic math. And yet zero still gets me

 

[gneill]

Yup. You fixed it!

 

[Ryan Walkowski]

Something else maybe you can enlighten me on. The paper that gives me all the variables shows Xc as -j40 now i was taking that complex number too literal and for long enough when i was calculating VC as in (Vc = Is x Xc) i was at first using the -j40 as a literal value for Xc so -40. I am right in saying that it is infact a whole number 40 you use rather than the complex form. I have pages of j notation but its a struggle to grasp when your working by yourself.

 

[gneill]

Technically, -j40 Ohms is the value of the impedance for the capacitor. It's a complex number that is purely imaginary (no real part).
The reactance of that capacitor is 40 Ohms, a real number which is the magnitude of the impedance.

Reactance and impedance are thus closely related. Typically formulas that use reactance values take care to use signs or operators (+ or -) in the expressions to handle the relationship between them, and separate the reactive parts from the real resistance parts, combining them using vector style math (square root of sum of squares style addition). On the other hand, formulas that use complex impedance just use standard complex arithmetic and no special considerations are necessary; Just write your equations as though everything is "resistance" and do the complex arithmetic.

Personally I dislike the use of "X" variable names for what are impedances because it can lead to confusion. Conventionally X represents reactance and Z impedance, so I would have called the impedances $Z_C$ and $Z_L$ with the understanding that they are complex values.

 

[Ryan Walkowski]

I have to agree with you on the use of X and instead Z but when i tried to submit that on a previous paper as quite honestly it made more sense to me i was told not to use them. The lecturers are rigid and very unhelpful. They throw big blocks of paperwork with no explained examples. I was asked to work out the power of something at the very start i used P=I2R and got zero marks as they were looking for P=VI when both are equally correct. Anyway thanks for your help its certainly helped!