A.C. fundamentals refer to the principles and concepts related to alternating current (A.C.) circuits. A series R-L-C circuit is a type of A.C. circuit that consists of a resistor (R), an inductor (L), and a capacitor (C) connected in series. Each component plays a specific role in the behavior of the circuit when alternating current is applied.
Here's a breakdown of each component and its behavior in a series R-L-C circuit:
Resistor (R):
The resistor opposes the flow of current in the circuit, converting electrical energy into heat.
In an A.C. circuit, the resistance causes a phase shift of 0 degrees between the voltage across the resistor and the current flowing through it.
Inductor (L):
The inductor stores energy in its magnetic field when current flows through it.
In an A.C. circuit, the inductor causes a phase shift of +90 degrees between the voltage across the inductor and the current flowing through it.
The inductive reactance (XL) depends on the frequency (f) of the alternating current and the inductance (L) of the coil: XL = 2πfL.
Capacitor (C):
The capacitor stores energy in its electric field when it's charged.
In an A.C. circuit, the capacitor causes a phase shift of -90 degrees between the voltage across the capacitor and the current flowing through it.
The capacitive reactance (XC) depends on the frequency (f) of the alternating current and the capacitance (C) of the capacitor: XC = 1 / (2πfC).
When you have a series R-L-C circuit with all three components connected in series, their individual reactances combine to create the overall impedance (Z) of the circuit. Impedance is a complex quantity, meaning it has both a magnitude and a phase angle. The impedance in a series R-L-C circuit can be calculated as follows:
Z = √(R^2 + (XL - XC)^2)
The phase angle (θ) between the applied voltage and the total current is given by:
θ = arctan((XL - XC) / R)
In this circuit, the phase angle indicates whether the current leads or lags behind the voltage.
Series R-L-C circuits have interesting behavior based on the frequency of the applied alternating current. At certain frequencies, the reactances of the inductor and capacitor can cancel each other out, resulting in a phenomenon called resonance. This leads to the circuit having a minimum impedance and maximum current flow.
Understanding the behavior of series R-L-C circuits is crucial in various fields, such as electrical engineering and electronics, where A.C. circuits are commonly used in applications like filters, tuning circuits, and impedance matching.