Reactance and impedance

Thread Starter

student777

Joined Jul 19, 2006
2
Someone please help! I am stuck on this problem and I dont understand the equation or how to apply it here. Please help?


a) The reactance of the inductor L.

b) The impedance of the resistor and inductor in series.



You do not need to find the phase of the current in this series circuit.




R1 = 10 Ω


L = 20 mH


E = 10 VAC
60 Hz
 

Papabravo

Joined Feb 24, 2006
12,765
The equation for inductive reactance is quite straightforward. The inductive reactance is a function of frequency and the inductance. The factor of 2*pi converts frequency in Hertz(cycles per second) to radians per second. A radian is a dimensionless measure of angular displacement. So
Rich (BB code):
X-sub-L = 2 * pi * f * L
        = 2 * 3.1415926 * 60 * 20 e -3
        = 7.54 Ohms
Impedance is a complex number with a Real and an Imaginary part. Individual components may have either a real or an imaginary part or both when modeling less than ideal components. So
Rich (BB code):
Z-sub-R  = 10 + j0
Z-sub-L  =  0 + j7.54
    and
Z-series = 10 + j7.54
For a resistor and an inductor in series you add the complex impedances. Another way to express the impeadance is as a magnitude and an angle.
Rich (BB code):
MAG = sqrt(10^2 + (7.54)^2) = 12.54 Ohms
ARG = arctan(7.54/10) = 37 degrees = .646 radians
 
The reactance of the inductor is 7.54ohms ( Xsub l = 2pi fl, however, the total circuit impedance in series is 7.54ohms + 10 ohms = 17.54 ohms. Impedance is the total opposition to AC, inductive reactance + capacitive reactance + resistance.
 

Papabravo

Joined Feb 24, 2006
12,765
The reactance of the inductor is 7.54ohms ( Xsub l = 2pi fl, however, the total circuit impedance in series is 7.54ohms + 10 ohms = 17.54 ohms. Impedance is the total opposition to AC, inductive reactance + capacitive reactance + resistance.
You can't add reactance to resistance. The algebra of complex numbers won't allow that. Resistances are always in the real part of the complex impedance. If the resistance in the wire in the inductor were measurable it would be added to the external series resistance. Reactances are always in the imaginary part. If the external series resistor was a wirewound with some small inductance, that reactance could be added to the reactance of the inductor.

Resistance and reactance are both real numbers. Impedance is a complex number and the algebra of complex numbers is different than the algebra of real numbers.
 
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