Effect of Frequency on Inductive Reactance

In an a.c. circuit, an inductor produces inductive reactance which causes the current
to lag the voltage by 90 degrees. Because the inductor "reacts" to a changing
current, it is known as a reactive component. The opposition that an inductor presents to
a.c. is called inductive reactance (X_{L}). This opposition is caused by the
inductor "reacting" to the changing current of the a.c. source. Both the
inductance and the frequency determine the magnitude of this reactance. This relationship
is stated by the formula:

As shown in the equation, any increase in frequency, or "f," will cause a
corresponding increase of inductive reactance, or "X_{L}." Therefore,
the INDUCTIVE REACTANCE VARIES DIRECTLY WITH THE FREQUENCY. As you can see, the higher the
frequency, the greater the inductive reactance; the lower the frequency, the less the
inductive reactance for a given inductor. This relationship is illustrated in figure 1-2.
Increasing values of X_{L} are plotted in terms of increasing frequency. Starting
at the lower left corner with zero frequency, the inductive reactance is zero. As the
frequency is increased (reading to the right), the inductive reactance is shown to
increase in direct proportion.

Figure 1-2. - Effect of frequency on inductive reactance.

Effect of Frequency on Capacitive Reactance

In an a.c. circuit, a capacitor produces a reactance which causes the current to lead
the voltage by 90 degrees. Because the capacitor "reacts" to a changing voltage,
it is known as a reactive component. The opposition a capacitor presents to a.c. is called
capacitive reactance (X_{C}). The opposition is caused by the capacitor
"reacting" to the changing voltage of the a.c. source. The formula for
capacitive reactance is:

In contrast to the inductive reactance, this equation indicates that the CAPACITIVE
REACTANCE VARIES INVERSELY WITH THE FREQUENCY. When f = 0, X_{C} is infinite and
decreases as frequency increases. That is, the lower the frequency, the greater the
capacitive reactance; the higher the frequency, the less the reactance for a given
capacitor.

As shown in figure 1-3, the effect of capacitance is opposite to that of inductance.
Remember, capacitance causes the current to lead the voltage by 90 degrees, while
inductance causes the current to lag the voltage by 90 degrees.

Figure 1-3. - Effect of frequency on capacitive reactance.

Effect of Frequency on Resistance

In the expression for inductive reactance, X_{L} = 2pfL,
and in the expression for capacitive reactance,

both contain "f" (frequency). Any change of frequency changes the reactance
of the circuit components as already explained. So far, nothing has been said about the
effect of frequency on resistance. In an Ohm's law relationship, such as R = E/I no
"f" is involved. Thus, for all practical purposes, a change of frequency does
not affect the resistance of the circuit. If a 60-hertz a.c. voltage causes 20
milliamperes of current in a resistive circuit, then the same voltage at 2000 hertz, for
example, would still cause 20 milliamperes to flow.

NOTE: Remember that the total opposition to a.c. is called impedance (Z). Impedance is
the combination of inductive reactance (X_{L}), capacitive reactance (X_{C}),
and resistance (R). When dealing with a.c. circuits, the impedance is the factor with
which you will ultimately be concerned. But, as you have just been shown, the resistance
(R) is not affected by frequency. Therefore, the remainder of the discussion of a.c.
circuits will only be concerned with the reactance of inductors and capacitors and will
ignore resistance.

A.c. Circuits Containing Both Inductive and Capacitive Reactances

A.c. circuits that contain both an inductor and a capacitor have interesting
characteristics because of the opposing effects of L and C. X_{L} and X_{C}
may be treated as reactors which are 180 degrees out of phase. As shown in figure 1-2, the
vector for X_{L} should be plotted above the baseline; vector for X_{C},
figure 1-3, should be plotted below the baseline. In a series circuit, the effective
reactance, or what is termed the RESULTANT REACTANCE, is the difference between the
individual reactances. As an equation, the resultant reactance is: _{}

X = X_{L} - X_{C}

Suppose an a.c. circuit contains an X_{L} of 300 ohms and an X_{C} of
250 ohms. The resultant reactance is:

X = X_{L} - X_{C} = 300 - 250 = 50 ohms (inductive)

In some cases, the X_{C} may be larger than the X_{ L}. If X_{L}
= 1200 ohms and X_{C} = 4000 ohms, the difference is: X = X_{L} - X_{C}
= 1200 - 4000 = -2800 ohms (capacitive). The total carries the sign (+ or -) of the
greater number (factor).

Q.1 What is the relationship between frequency and the values of (a) X_{L}, (b)
X_{C}, and (c) R?

Q.2 In an a.c. circuit that contains both an inductor and a capacitor, what term is used
for the difference between the individual reactances?