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Which is true for series resonance?
Z=R
XLтАЛ=XCтАЛ
I=RVтАЛ
All of above
All of above
In an RLC series circuit, resonance occurs when the inductive reactance equals the capacitive reactance, causing them to cancel each other out. This results in the circuit behaving as a purely resistive load, where impedance is minimum and current is maximum.
In an RLC series circuit, resonance occurs when the inductive reactance equals the capacitive reactance, causing them to cancel each other out. This results in the circuit behaving as a purely resistive load, where impedance is minimum and current is maximum.
XLтАЛ=2╧АfrтАЛL тАФ Inductive Reactance
XCтАЛ=2╧АfrтАЛC1тАЛ тАФ Capacitive Reactance
Z=R2+(XLтАЛтИТXCтАЛ)2тАЛ тАФ Total Impedance
frтАЛ=2╧АLCтАЛ1тАЛ тАФ Resonant Frequency
The inductive reactance XLтАЛ=2╧АfL increases with frequency, while capacitive reactance XCтАЛ=2╧АfC1тАЛ decreases. At the resonant frequency frтАЛ, these magnitudes equalize (XLтАЛ=XCтАЛ), nullifying the imaginary part of the impedance Z=R+j(XLтАЛтИТXCтАЛ). Consequently, the total impedance Z simplifies to the resistance R, and the circuit power factor becomes unity.
At resonance, the phase angle between voltage and current is zero.
The circuit provides minimum impedance to the source at the resonant frequency.
Voltage magnification occurs across the inductor and capacitor.
The circuit acts as a band-pass filter configuration.
Maximum current flow for a given voltage source
Selectivity in radio tuning circuits
Risk of voltage breakdown due to high Q-factor
Sensitive to frequency variations
Radio frequency tuning circuits
Band-pass filter designs
Induction heating systems
The Q-factor (Quality Factor) determines the sharpness of the resonance curve: Q=R1тАЛCLтАЛтАЛ.
If XLтАЛ>XCтАЛ, the circuit is inductive (lagging pf); if XCтАЛ>XLтАЛ, it is capacitive (leading pf).
D is correct тАФ All listed conditions (Z=R, XLтАЛ=XCтАЛ, I=V/R) define the state of resonance in an RLC series circuit.
Always remember that resonance in series circuits leads to minimum impedance, while in parallel circuits, it leads to maximum impedance.