How does resonance occur in a series RLC circuit?
1 Answer
Resonance occurs in a series RLC (Resistor-Inductor-Capacitor) circuit when the inductive reactance (XL) and capacitive reactance (XC) have equal magnitudes but opposite signs, cancelling each other out. At resonance, the net reactance becomes zero, and the impedance of the circuit is purely resistive. This results in a maximum current flow through the circuit and is accompanied by specific voltage and current relationships.
Let's break down the components and the phenomenon of resonance in a series RLC circuit:
Resistor (R): The resistor is a passive element that limits the current in the circuit and dissipates energy in the form of heat.
Inductor (L): The inductor stores energy in its magnetic field when current flows through it. Its reactance (XL) is given by the formula XL = 2πfL, where f is the frequency of the alternating current and L is the inductance of the coil.
Capacitor (C): The capacitor stores energy in its electric field. Its reactance (XC) is given by the formula XC = 1 / (2πfC), where f is the frequency of the alternating current and C is the capacitance of the capacitor.
At resonance:
XL = XC
2πfL = 1 / (2πfC)
Solving for the resonant frequency (f_res):
f_res = 1 / (2π√(LC))
When the frequency of the applied AC voltage matches the resonant frequency (f_res) of the RLC circuit, the reactances cancel each other out, resulting in a purely resistive impedance. This means that the impedance of the circuit is at its minimum value, allowing the maximum current to flow through the circuit. The resonance causes the current to be in-phase with the voltage across the circuit.
In a series RLC circuit, at resonance:
Current (I) is at its maximum value.
Voltage across the resistor (VR) is in phase with the current.
Voltage across the inductor (VL) leads the current by 90 degrees.
Voltage across the capacitor (VC) lags the current by 90 degrees.
Applications of resonance in RLC circuits include frequency-selective filters and various tuning applications in electronic devices. Understanding resonance is essential to optimize the performance of these circuits and to avoid unwanted effects due to resonance in practical applications.
Let's break down the components and the phenomenon of resonance in a series RLC circuit:
Resistor (R): The resistor is a passive element that limits the current in the circuit and dissipates energy in the form of heat.
Inductor (L): The inductor stores energy in its magnetic field when current flows through it. Its reactance (XL) is given by the formula XL = 2πfL, where f is the frequency of the alternating current and L is the inductance of the coil.
Capacitor (C): The capacitor stores energy in its electric field. Its reactance (XC) is given by the formula XC = 1 / (2πfC), where f is the frequency of the alternating current and C is the capacitance of the capacitor.
At resonance:
XL = XC
2πfL = 1 / (2πfC)
Solving for the resonant frequency (f_res):
f_res = 1 / (2π√(LC))
When the frequency of the applied AC voltage matches the resonant frequency (f_res) of the RLC circuit, the reactances cancel each other out, resulting in a purely resistive impedance. This means that the impedance of the circuit is at its minimum value, allowing the maximum current to flow through the circuit. The resonance causes the current to be in-phase with the voltage across the circuit.
In a series RLC circuit, at resonance:
Current (I) is at its maximum value.
Voltage across the resistor (VR) is in phase with the current.
Voltage across the inductor (VL) leads the current by 90 degrees.
Voltage across the capacitor (VC) lags the current by 90 degrees.
Applications of resonance in RLC circuits include frequency-selective filters and various tuning applications in electronic devices. Understanding resonance is essential to optimize the performance of these circuits and to avoid unwanted effects due to resonance in practical applications.