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In a series RLC circuit, at resonance frequency, the phase angle between voltage and current is:
90 degrees
45 degrees
0 degrees
180 degrees
0 degrees
At the resonance frequency of a series RLC circuit, the inductive reactance (XLтАЛ) exactly equals the capacitive reactance (XCтАЛ), causing the net reactance of the circuit to become zero. Consequently, the circuit behaves as a purely resistive load, resulting in the current being in phase with the applied voltage.
At the resonance frequency of a series RLC circuit, the inductive reactance (XLтАЛ) exactly equals the capacitive reactance (XCтАЛ), causing the net reactance of the circuit to become zero. Consequently, the circuit behaves as a purely resistive load, resulting in the current being in phase with the applied voltage.
frтАЛ=2╧АLCтАЛ1тАЛ тАФ Resonance frequency formula
╧Х=tanтИТ1(RXLтАЛтИТXCтАЛтАЛ) тАФ Phase angle formula
XLтАЛ=2╧АfL тАФ Inductive reactance
XCтАЛ=2╧АfC1тАЛ тАФ Capacitive reactance
In an RLC series circuit, the total impedance is Z=R2+(XLтАЛтИТXCтАЛ)2тАЛ. At resonance, the condition XLтАЛ=XCтАЛ (or ╧ЙL=╧ЙC1тАЛ) is met, which minimizes impedance to Z=R. Since the imaginary component of the impedance is zero, the phase angle ╧Х=tanтИТ1(RXLтАЛтИТXCтАЛтАЛ) becomes 0┬░.
At resonance, the power factor of the circuit is unity (cos╧Х=1).
The impedance is minimum and equal to the resistance R at the resonance frequency.
The circuit current reaches its maximum value at the resonance frequency.
Resonance only occurs when the circuit is in series combination.
Maximum power transfer occurs at resonance.
Highly selective frequency response in tuning circuits.
High currents near resonance can damage components if not properly designed.
Voltage magnification across reactive components can lead to insulation stress.
Radio and television tuning circuits.
Band-pass filter designs.
The phase angle is positive (lagging) when XLтАЛ>XCтАЛ and negative (leading) when XCтАЛ>XLтАЛ.
Option A (90 degrees) is valid for a pure inductor or capacitor only.
Option B (45 degrees) occurs when R=XLтАЛтИТXCтАЛ.
Option D (180 degrees) is not physically possible for a simple series RLC circuit.
C is correct тАФ At resonance, the total reactance is zero, making the circuit purely resistive and the phase angle between voltage and current 0┬░.
Always remember that resonance in a series circuit implies Unity Power Factor; this is a frequently tested concept in all electrical engineering exams.