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In a series RLC circuit at resonance, the phase angle between the voltage and current is:
90 degrees
45 degrees
0 degrees
180 degrees
0 degrees
At resonance in a series RLC circuit, the inductive reactance equals the capacitive reactance, causing the net reactance to become zero. Consequently, the circuit behaves as a purely resistive load where the voltage and current are perfectly in phase.
At resonance in a series RLC circuit, the inductive reactance equals the capacitive reactance, causing the net reactance to become zero. Consequently, the circuit behaves as a purely resistive load where the voltage and current are perfectly in phase.
XLтАЛ=2╧АfL тАФ Inductive reactance formula
XCтАЛ=2╧АfC1тАЛ тАФ Capacitive reactance formula
frтАЛ=2╧АLCтАЛ1тАЛ тАФ Resonant frequency formula
╧Х=tanтИТ1(RXLтАЛтИТXCтАЛтАЛ) тАФ Phase angle formula
In a series RLC circuit, resonance occurs when the supply frequency equals the natural frequency of the circuit. At this frequency, the voltage drop across the inductor VLтАЛ and the capacitor VCтАЛ are equal in magnitude but 180┬░ out of phase, effectively canceling each other out. This leaves only the ohmic resistance R in the circuit, resulting in a phase angle ╧Х=0 between the source voltage and the line current.
At resonance, impedance Z is minimum and equal to resistance R.
Power factor of a series RLC circuit at resonance is unity (1).
Current in the circuit is at its maximum value.
The circuit becomes purely resistive.
Maximum power transfer efficiency at resonance.
Used in selective frequency tuning circuits (like radio receivers).
High currents can lead to overheating in components.
Risk of voltage magnification across reactive components (VLтАЛ and VCтАЛ can exceed supply voltage).
Radio frequency (RF) tuning circuits.
Oscillators and band-pass filters.
For option A (90 degrees), this occurs in purely inductive or purely capacitive circuits.
For option B (45 degrees), this occurs when R=XLтАЛтИТXCтАЛ.
For option D (180 degrees), this is not possible in a standard series RLC circuit as the phase angle is bounded between тИТ90┬░ and +90┬░.
C is correct тАФ At resonance, inductive and capacitive reactances cancel out, leaving the circuit purely resistive with a phase angle of 0 degrees.
Remember that at resonance, the phase angle is always 0┬░, power factor is always 1, and impedance is always equal to R, regardless of the individual values of L and C.