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Impedance of simple networks

Impedance of 2 elements in series is a complex number. Impedance terminology: reactance, susceptance, admittance. Created by Willy McAllister.

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• So if we have a capacitor and inductor which have the same value of reactance in a RLC series then the vector addition of the two will make it zero and that would basically mean that the impedance is equal to the resistance in the resistor?
• Hello Brine,

Correct!

If you have a series RLC and the L and C have the same (but opposite sign) impedance then yes, the L and C will effectively cancel each other out. The circuit will appear resistive. This is known as a "series resonant" circuit.

If you want to have some fun calculate the voltage drop across each element. You might be surprised. Another challenge is to determine what happens in a parallel resonant circuit (R, L, and C are all in parallel).

Excellent question - keep up the good work! Do leave a comment below if you want to continue this conversation.

Regards,

APD
• How do you add impedance for components that are in parallel?
(1 vote)
• in phasor representation of impedance, what does the phase angle represent? does it represent phase difference between resistance and reactance?
(1 vote)
• When you have any two sine waves you can talk about the timing relationship between them in terms of their phase difference. When you couple the phase angle with the magnitude of the sine waves, you pretty much know everything there is to know about them. We worked out the impedance of R, L, and C we discovered the phase difference between the voltage sine wave and the current sine wave was either 0, +90, or -90 (for R, L, C respectively).
• Why do you draw current direction? Isn't this an AC network?
(1 vote)
• The current arrow and the nearby voltage polarity signs indicate the reference directions for both current and voltage. You are correct that current flows both ways in an AC circuit. But at any one instant in time the current has a particular direction. You can leave out voltage and current signs in AC diagrams if you want. It typically doesn't hurt. However, if you are working with a power supply circuit you need to be careful. At some point in the circuit you will begin to have DC waveforms.
• How would I determine the
frequency at which the impedance is a real number?
(1 vote)
• What is the impedance value of a capacitor in series with an inductor and how would you find the phase angle and the output voltage for a circuit like this?
(1 vote)
• You sir are a class act! You make things easy to understand, thank you!
(1 vote)
• in the last bit, is the hypotenuse the value for 1/wc ? or where did 1/wc end up?
(1 vote)
• At the very end the hypotenuse is Z = jwL + R + 1/jwC.

The capacitor vector points straight down with magnitude 1/wC. That's the third vector I drew while doing the vector sum.
(1 vote)