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An inductor rated at 4 Henrys is subjected to a sinusoidal AC voltage of 24 volts RMS, at a frequency of 60 hertz. Write the formula for calculating inductive reactance (X L), and solve for current through the inductor.
Inductive reactance is the property of an inductive coil that resists the change in alternating current (AC) through it and is similar to the opposition to direct current (DC) in a resistance.
Complex Impedance. The ratio of the voltage across a component to the current through it when both are expressed in complex notation. I=I0sin(ωt) I=I0ejωt.
\(X_L\) is defined to be the inductive reactance, given by \[X_L = 2\pi fL,\] with \(f\) the frequency of the AC voltage source in hertz. Inductive reactance \(X_L\) has units of ohms and is greatest at high frequencies.
Inductive Reactance. Capacitive Reactance. Impedance in relation to R and X. Z L = R + jX L. Z C = R - jX C. Ohm’s Law for AC. Series and Parallel Impedances. All impedances must be calculated in complex number form for these equations to work. Resonance. This equation applies to a non-resistive LC circuit.
Inductors and Inductive Reactance. Suppose an inductor is connected directly to an AC voltage source, as shown in Figure 23.45. It is reasonable to assume negligible resistance, since in practice we can make the resistance of an inductor so small that it has a negligible effect on the circuit.
In particular, if a coil rotates in the presence of a magnetic field, the induced emf varies sinusoidally with time and leads to an alternating current (AC), and provides a source of AC power. The symbol for an AC voltage source is .
