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-cor…
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.
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Q1: Why does current lag voltage in an inductor connected to an AC source?
In an AC circuit, the inductor's self-induced back EMF opposes current changes. Using Kirchhoff's loop rule and integrating the voltage equation reveals that current reaches its maximum positive value one-quarter cycle after voltage peaks. This phase relationship means the current lags the voltage by 90 degrees, a fundamental characteristic of pure inductors in alternating current.
Q2: What is inductive reactance and how does it relate to frequency?
Inductive reactance is the AC resistance offered by an inductor, calculated as the ratio of peak voltage to peak current and measured in ohms. It depends directly on the frequency of the AC source: higher frequencies produce greater inductive reactance, while lower frequencies produce less. This frequency dependence distinguishes inductive reactance from DC resistance.
Q3: How can phasor diagrams represent the relationship between inductor voltage and current?
Phasor diagrams show voltage and current as rotating vectors at the same angular frequency. The current phasor lags behind the voltage phasor by π/2 radians (90 degrees), visually representing their phase relationship. Both phasors rotate together, making phasor diagrams an effective tool for analyzing AC inductor behavior and comparing it with other circuit components.
Q4: What physical components make up an inductor and how do they store energy?
An inductor consists of coils or loops of wire wound around a hollow former or ferromagnetic material like iron to increase inductance. When voltage is applied across the inductor's terminals, a magnetic field is created where the inductor stores energy. The self-induced back EMF controls current growth until it reaches steady state, where the back EMF decays to zero.
Q5: How does an inductor's behavior differ between DC and AC circuits?
In DC circuits, an inductor's current rises until back EMF decays to zero, then flows freely. In AC circuits, the inductor continuously opposes current changes through inductive reactance, which depends on frequency and inductance. The AC resistance is represented as a complex number and measured in ohms, distinguishing it from simple DC resistance through the term reactance or impedance.
Q6: What role does back EMF play in controlling current through an inductor?
Back EMF is the self-induced voltage that opposes current changes in an inductor. It is proportional to the rate of current variation through the coil. In DC circuits, back EMF decays as current stabilizes; in AC circuits, it continuously opposes current flow, creating the phase lag and reactance that characterize inductor behavior.
Q7: How can Kirchhoff's loop rule be applied to find current in an AC inductor circuit?
Kirchhoff's loop rule states that the sum of potential differences around a closed loop equals zero. For an inductor, the instantaneous voltage across it can be determined using this rule and the EMF relationship. Integrating the resulting voltage equation yields the instantaneous current, which reveals the phase lag and allows calculation of inductive reactance.