Calculating Impedance and Drawing a Basic Phasor Diagram

[maherelharake]

Homework Statement

I have attached the problem and all my work. If someone can check my work for part a, that would be great. As far as part b, I need the most help here. Finally for part c, I think my work so far is correct, but I need help to graph it. Thank you in advance.

Homework Equations

The Attempt at a Solution

 

[Claude Bile]

The numbers for part a) look correct, though you should express the reactance of the capacitor in the form a+jb by multiplying top and bottom by j. Also, don't forget units (ohms).

The phasor diagram is straightforward, simply plot the three reactances as vectors on the complex plane.

For part c), you have made an error on the fourth line of working (taking magnitudes). You cannot take the magnitude of each individual term on the RHS as you have done. You need to rearrange the RHS in the form a+ib first, then take the magnitude as sqrt(a^2+b^2).

Claude.

 

[maherelharake]

Ok I think I took care of part a.

As far as b, it says to plot the reciprocal reactances. Does that mean that the Resistor Reactance is along the x-axis (Real axis) and the other two are plotted along the y axes (imaginary axis)?

For c, I am struggling to get it in that form. For the form a+ib, I can't collect the imaginary terms and get it in that form. Any pointers?

Thanks again.