The Amateur Extra class question of the week comes from sub-element 5 (electrical principles) section C (polar coordinates) [E5C06]
In polar coordinates, what is the impedance of a network consisting of a 100-ohm-reactance capacitor in series with a 100-ohm resistor?
A. 121 ohms at an angle of -25 degrees
B. 191 ohms at an angle of -85 degrees
C. 161 ohms at an angle of -65 degrees
D. 141 ohms at an angle of -45 degrees
We need to remember how to plot polar coordinates when it comes to impedance. First we must plot the given points on an X-Y graph.
We plot pure resistance on the horizontal, or X axis. Then we plot the reactive component on the vertical or Y axis. But we have to remember that capacitive reactance needs to be plotted on the negative. The result is a point at coordinates (100,-100) on the graph, on the above image, it would be at point M, (only point M would be BELOW the X axis, not above!) (I need to get a proper graph of this, if you read this message, please remind me!)
to find the magnitude of the impedance, we employ Mr. Pythagoras’ thereom as so:
or
we could bother with using trigonometry to find the angle, but since both components are of the same magnitude, we know that its 45°. Actually, since it’s below the X axis, its actually negative, or -45°.
Therefore, the answer is D. 141 ohms at an angle of -45 degrees
