A.C. fundamentals refer to the principles and concepts related to alternating current (A.C.) circuits. An A.C. circuit that contains only inductance refers to a circuit composed solely of inductors. An inductor is a passive electronic component that stores energy in the form of a magnetic field when current flows through it.
Here are some key points about A.C. circuits containing inductance:
Inductor Basics: An inductor is typically represented by the symbol "L" in circuit diagrams. It consists of a coil of wire wound around a core, which can be made of various materials. The inductor opposes changes in the current flowing through it by inducing a voltage across its terminals according to Faraday's law of electromagnetic induction.
Reactance: In an A.C. circuit, the opposition to the flow of alternating current due to the presence of inductance is called inductive reactance (denoted as "XL"). Inductive reactance depends on the frequency of the alternating current and the value of the inductance. The formula for inductive reactance is:
XL = 2πfL
where:
XL is the inductive reactance
π (pi) is approximately 3.14159
f is the frequency of the A.C. signal in Hertz (Hz)
L is the inductance in Henrys (H)
Phasors: A.C. circuits involving inductors are often analyzed using phasors, which are complex numbers representing the amplitude and phase of the A.C. quantities. The phase relationship between voltage and current in an inductor is such that the current lags behind the voltage by a phase angle of 90 degrees.
Impedance: Impedance is the overall opposition that a circuit offers to the flow of alternating current. In a circuit containing only inductance, the impedance is purely inductive and is denoted by "ZL." The impedance of an inductor can be calculated using the formula:
ZL = jXL
where j is the imaginary unit (j^2 = -1).
Voltage-Current Relationship: The voltage across an inductor is proportional to the rate of change of current through it. Mathematically, this relationship can be expressed as:
v(t) = L * di/dt
where:
v(t) is the voltage across the inductor at time t
L is the inductance
di/dt is the rate of change of current with respect to time
Phase Relationship: In an inductive circuit, the current lags behind the voltage by 90 degrees. This lagging phase relationship between current and voltage is characteristic of purely inductive circuits.
Understanding A.C. circuits with inductance is essential for analyzing and designing various electrical systems, especially those involving motors, transformers, and other devices that utilize inductive components.