How calculate impedance of series resonance LCR circuit?

Question

How we calculate impedance of LCR circuit? is we igonre Xc & Xl cos they are same? how we draw phase diagram?

Im diploma student hence we still dont use j factor, ( Advance math) but from these answers i got idea that purely Z=R or impedance equal to resistence. am i correct?

Answer 1

using the j operator, and w to represent angular frequency,
Z = R + jwL - i/jwC
When |Xc| and |Xl|, Z = R
To draw a phase diagram, plot R as + horizontal, Xl as + vertical, and Xc as - vertical. Z is the resultant.

Answer 2

Helmut has it correct. This occurs when wL = 1/wC. The frequency in radians/sec then becomes w = (LC)^-1/2 ... in other words, the square root of 1/LC. At resonance, these terms cancel out and you are left with a purely real impedance = resistance of the circuit which has a phase angle of 0.

The phase angle at resonance can be plotted on the complex plane where the x axis represents real numbers (R) and the y axis represents imaginary numbers (Xc and Xl). Since Xc and Xl are equal with opposite phase (+j and -j = +90 degrees and -90 degrees), they cancel out leaving only R on the plot with a phase angle of 0 degrees since R remains on the x axis and the phase angle is found as the angle from the postive x axis to the plotted point on the complex plane.

Bode plots do not really apply since we do not know values of L and C and the relationship makes a big difference in the full plot of angle or magnitude versus frequency and the question was for resonance which we know will be 0 degrees since it is purely real impedance at resonance.

Answer 3

Series Resonance Calculator

Answer 4

You can just add impedance in series- R value for resistors, jwL for inductors,1/(jwC) for capacitors, and don't forget phase. (Where w is frequency, C is capacitance, L is inductance, R is resistance, and j is the imaginary number sqrt(-1)

A phase diagram has frequency on the x-axis and phase on the y-axis; you can use a Bode plot

Answer 5

Xl - Xc = 0, thus resistive. This is the maximum current, as there is no reactance. A resistive load has a unity power factor Answer is (b) current is maximum, power factor is unity Edit: Since your post received 3 thumbs up...Anita could you please explain how current is at a minimum for series LCR when Xc cancels out Xl?

Answer 6

not sure