How do you determine the frequency at which a 1 uF capacitor & a 10 mH inductor will have the same reactance?

Question

What exactly is reactance anyways? the book is not too clear.

Answer 1

There is a handy formula for calculating the resonance of a tank circuit.

f = 1/((2*pi)*sqrt(L*C)) in Hz.

f = 1/(6.28*sqrt((1e-2)*(1e-6)))

f = 1.59 kHz

The Impedance of a circuit element is composed of two parts. A magnitude and a phase angle. The magnitude of the impedance is the ratio of the voltage waveform magnitude to the current waveform magnitude, and the phase angle is the difference between the phase of the voltage across a circuit element and the phase of the current through the element. Complex numbers have a magnitude and phase angle and are sufficient to describe a sinusoid at a single known frequency. The complex Impedance can also be viewed as real and imaginary parts. The real part (resistance) represents the ratio of the voltage component that is in-phase with the current to the total current magnitude. The imaginary part (reactance) represents the ratio of the voltage orthogonal to the current to the current magnitude. So, you are splitting the voltage into two vector components, one with the same phase as the current, and one 90 deg offset from the phase of the current. Average Power is dissopated for the resistive part of the impedance, because the voltage and current are in-phase for this part. Average Power is not dissopated for the reactive part of the impedance because the voltage is 90 deg out of phase with the current. The 90 deg phase shift comes from the I-V relationship of the Inductor and capacitor. That is why these components only have a reactive part (in the ideal case).

Answer 2

I'll try and answer your second questions. Reactance is a quality in a circuit element to limit the current for for a given voltage based on the frequency of the voltage. Resistance does the same thing, but resistance does it by dissipating power and producing heat. I light bulb or a toaster are two obvious examples.

A reactance is the characteristic to limit current of an a.c. signal voltage by a capacitor or an inductor (coil) but there's no heat produced.... it's lossless in the ideal case. This happens because these elements cause the current to lead or lag the voltage. They're not in the same phase and power is not dissipated. .The "reactive" elements don't dissipate power, they store it and return it to the system later. One element cause the current to take on one phase (current leads voltage) the other has current lagging the voltage . When the ractances (lead and lag) cancel, they have the same impedance and the elements seem to dissappear from the circuit. Hope this helps.