To arrive at impedance (aka Z), simply take the pathagorean sum of the hypotenuse of the Xc+Xl vector and R vector which mathimatically is:

Z = SQRT(R^2 + (Xc+Xl)^2);

Electrical engineers like to express this as the complex number equation “Z = R – jXc” when the LCR node is net capacitive, and as “Z = R + jXl” when the LCR node is net inductive, or as “Z=R” when the LCR is purely resistive as in the case of electrical resonance.

F#ck thinking thinking that way. Complex numbers just confuse the issue. Really, there are NO imaginary numbers involved in computing impedance. Both Xc and Xl are not imaginary at all but are very real and easily measured in absolute terms as is R.

To compute Xc:

Xc = 1/(2*pi*F*C), where F is frequency in cycles and C is capacitance in Farads.

To compute Xl:

Xc = (2*pi*F*L), where F is frequency in cycles and L is capacitance in Henries.

Resonance always occurs where Xc=Xl, meaning where 1/(2*pi*F*C) = (2*pi*F*L). Solving for resonant frequency F, the formula for resonance becomes:

F = 1/2*pi*L*C.

]]>So, I’m still not convinced that it is more relevant to require students to know complex numbers than to understand binary and base systems or formal logic with Boolean algebra. I believe it is far more likely students will run into these discreet math concepts than complex numbers. Or maybe math should be specialized sooner, so that those who are going into traditional engineering get the traditional mathematics path, and those going into ICT get a discreet mathematics path, and those going into nearly any other field get a statistical/probability path. Data from the Bureau of Labor statistics backs this up also, with the number of jobs in ICT being far higher than traditional engineering.

]]>Anyone working with radio or audio electronics is dealing with complex numbers, aware or not. ðŸ™‚

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