32.5:
Inductor in an AC Circuit
Consider an inductor connected across an alternating current voltage source. Using Kirchhoff's loop rule, the instantaneous voltage across the inductor can be determined.
Recalling the EMF across the inductor and considering the voltage around the loop as zero, the potential difference across the inductor can be established, and, by integrating the equation, the current through the inductor can be determined.
When the current and voltage quantities are plotted together, the current through the inductor lags the voltage across the inductor by a quarter of a cycle.
The relationships between instantaneous current and voltage can be represented using phasor diagrams, where both the phasors rotate at the same angular frequency, with the current phasor lagging behind the voltage phasor by π by 2 radian.
The ratio of peak voltage to peak current gives the inductive reactance of the inductor and is measured in ohms.
The inductive reactance of the inductor depends directly on the frequency of the alternating current source, with a high frequency leading to high inductive reactance and vice versa.
32.5:
Inductor in an AC Circuit
The basic components of an inductor are coils or loops of wire that are either wound around a hollow tube former or a ferromagnetic material (iron-cored) to increase their inductive value or inductance. When a voltage is applied across an inductor's terminals, a magnetic field is created, where the inductor stores its energy. The inductor's own self-induced or back emf value controls the growth of the current flowing through it. This back emf voltage is proportional to the rate of variation of the current flowing through an inductor coil. The current continues to rise until it reaches its maximum steady state condition, where the self-induced back emf has decayed to zero.
However, the behavior of an inductor's current flow in an alternating current (AC) circuit that contains an AC inductance differs significantly from that of a steady state direct current voltage. In an AC circuit, the resistance to the current flowing through the coil windings depends on the coil's inductance and the applied voltage waveform as it changes from positive to negative values. The coil's AC resistance, which is represented by a complex number, determines the actual resistance to the current flowing through the coil in an AC circuit. However, the term "reactance" is used to differentiate between a DC resistance value and an AC resistance value, also referred to as impedance. However, it is measured similarly to resistance in ohms. To distinguish it from a purely resistive load, the reactance of an inductor is called the inductive reactance, which is measured in Ohms and denoted with XL. The inductive reactance varies directly with the frequency of the AC source—a high frequency causes high inductive reactance.
In a simple circuit consisting of a pure inductor connected to an AC source, the applied voltage reaches its maximum positive value one-quarter of a cycle earlier than the current reaches its maximum positive value. Hence, the relationship between voltage and current can be understood using a phasor diagram, where the current lags the voltage by one-quarter of a cycle, or 90 degrees.
Suggested Reading
- OpenStax. (2019). University Physics Vol. 2. [Web version], Pg 394 – 396. Retrieved from https://openstax.org/books/university-physics-volume-2@8ede2ba/pages/15-2-simple-ac-circuits