AC Behavior of Capacitors and Inductors
Impedance
For DC circuits, Ohms Law applies directly to resistors , in AC circuits,
on the other hand, the current-voltage relationship is changed to this
form:
I=E/Z as compared to ohm's law I=E/R
(Z is the symbol for Impedance)
where I and E are the rms or "effective" values. For a simple resistor, Z = R.
Capacitive Reactance
A capacitors opposition to current flow is called capacitive reactance.
It is usually represented by XC.
XC =1/2pi fC f is frequency and C is the capacitance.
Notice that the capacitive reactance is inversely proportional to frequency
and capacitance.
Inductive Reactance
An inductors opposition to current flow is called inductive reactance.
It is usually represented by XL. XL=2pi fL f is frequency again and L
is the inductance. Notice that the inductive reactance is proportional
to frequency and Inductance.
You may be able to see this relationship in this reactance chart from
an old ARRL Handbook.
The darker lines slanting to the right are values of inductance. The lines
slanting to the left are capacitance.
Resonance
A LC circuit in which the inductive and capacitive reactances are equal is said to be resonant
Resonance in an electronic circuit is like ringing a bell. If you hit
a bell with a hammer it rings at its natural frequency which is determined
by the material and the shape of the bell. In an inductor/capacitor (LC)
circuit like in the Tesla coil the number of turns in the primary coil
and the value of the tank capacitor determine the frequency of ringing.
The ringing occurs because of a trading of energy back and forth between
the capacitor and the coil. Again, the rate at which this happens is due
to the value of the capacitance and the impedance of the coil. The Secondary
coil has a significant stray capacitance and a large electrode, which
acts as a capacitor. The combination of the inductor, its distributed
capacitance and the top load creates a self-resonant coil. The secondary
is an inductor which in itself can store energy as described earlier.
The stray capacitance and the topload act as a single capacitor in parallel
with the secondary inductor. This creates a resonant circuit where energy
can be traded back an forth at a specific frequency based on the value
of inductance and the value of total capacitance. The secondary topload
and stray capacitance is a small value of capacitance measured in pico-farads.
The secondary coil has a fairly high inductance as compared to the Primary.
The low inductance primary can be made to resonate at the same frequency
as the secondary by connecting a high value of capacitance.
The formula for resonance in an LC circuit is:
Fr=1/2pi * sqrt(L*C)
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