What Is the Phase Angle in a Low Resistance L-C Series Circuit?

In summary, in an L-C series circuit with very small resistance, the phase angle is -90 degrees as the voltage across the capacitor is higher than across the inductor, resulting in a negative tangent. This is because the cosine, which is proportional to the resistance, is positive and the tangent tends to negative infinity as the resistance approaches zero. The tangent of -90 degrees is undefined, but the limit is infinite. The real part of the complex impedance, R, cannot be negative and the imaginary part, X, is equal to XL-XC. The phase angle can be calculated as the arctangent of X/R, which is only defined if R is finite.
  • #1
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Phase angle?? L-C series

Homework Statement


In an L-C series circuit with very small resistance, the voltage drops across inductor and capacitor are 100V and 120V,. What's the phase angle?


Homework Equations


tantheta= Xl -Xc)/ R


The Attempt at a Solution



According to book's explanation, tantheta= (Xl -Xc)/ R is infinity..!??

Why?? and the answer is -90degree...
Please explain!:)
 
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  • #2


XL-XC is negative as the voltage across the capacitor is higher than across the inductor. So the tangent is negative: the angle itself is negative, as its cosine (which is proportional to R) is positive. R is very small, so the tangent is very large, tends to -infinity as R tends to zero. What is the tangent of -90 degree?

ehild
 
  • #3


ehild said:
XL-XC is negative as the voltage across the capacitor is higher than across the inductor. So the tangent is negative: the angle itself is negative, as its cosine (which is proportional to R) is positive. R is very small, so the tangent is very large, tends to -infinity as R tends to zero. What is the tangent of -90 degree?

ehild

as its cosine is positive?!? what do you mean??

tan(-90) is ERR: DOMAIN on my calculator lol...
 
  • #4


Have you seen a tangent function plotted out? how does it look very close to 90 degree?

The limit is infinite, if you calculate the tangent of angles closer and closer to 90 degree with your calculator. Try.

The real part of the complex impedance is R; it can not be negative.

The imaginary part is called reactance and denoted by X. For a series circuit, X=XL-XC.

If Z is the magnitude of the complex impedance, and theta is its phase angle, then R=Z*cos(theta), X=Z*sin(theta).


X/R= Z*sin(theta)/(Z*cos(theta))= sin(theta)/cos(theta)=tan (theta)

As R >=0, the cosine of the phase angle is positive: The angle must be between -90degree and 90 degree.

As tan(theta)=X/R, you can calculate the angle as the arctangent of X/R if R is finite. If it is zeo, the angle is either 90 of -90 degree.

ehild
 

Related to What Is the Phase Angle in a Low Resistance L-C Series Circuit?

What is phase angle?

Phase angle is a measurement of the time difference between two periodic signals or waveforms. It is typically measured in degrees and represents how far the two signals are out of sync with each other.

How is phase angle calculated?

Phase angle is calculated by taking the difference in phase between two signals or waveforms and expressing it in degrees. This is often done using trigonometric functions such as sine, cosine, and tangent.

What is the significance of phase angle in L-C series circuits?

In L-C series circuits, phase angle is used to determine the relationship between the voltage and current in the circuit. It indicates whether the circuit is capacitive or inductive, and helps to determine the power factor and efficiency of the circuit.

How does phase angle affect power transfer in L-C series circuits?

In L-C series circuits, a phase angle of 0 degrees indicates maximum power transfer, while a phase angle of 90 degrees indicates zero power transfer. This means that the closer the phase angle is to 0 degrees, the more efficient the power transfer will be.

Can phase angle be negative?

Yes, phase angle can be negative. A negative phase angle indicates that one signal is lagging behind the other, while a positive phase angle indicates that one signal is leading the other. Negative phase angles are common in inductive circuits.

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