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Frequency for parallel resonance is given by
f = 2╧А тИЪLC
f = 2╧А тИЪL/C
f = 1/(2╧А тИЪL/C)
f = тИЪL/C
f = 1/(2╧А тИЪL/C)
The resonant frequency for a parallel LC circuit is the frequency at which the inductive reactance (XLтАЛ) equals the capacitive reactance (XCтАЛ), causing the reactive components of the currents to cancel out. This results in the circuit appearing purely resistive to the source.
The resonant frequency for a parallel LC circuit is the frequency at which the inductive reactance (XLтАЛ) equals the capacitive reactance (XCтАЛ), causing the reactive components of the currents to cancel out. This results in the circuit appearing purely resistive to the source.
XLтАЛ=2╧АfL тАФ Inductive Reactance
XCтАЛ=2╧АfC1тАЛ тАФ Capacitive Reactance
frтАЛ=2╧АLCтАЛ1тАЛ тАФ Parallel Resonant Frequency
In a parallel circuit containing an inductor and a capacitor, the impedance is at its maximum at resonance. The condition for resonance is defined by setting XLтАЛ=XCтАЛ, which leads to 2╧АfL=2╧АfC1тАЛ. Solving this algebraic equation for f yields the formula f=2╧АLCтАЛ1тАЛ.
At resonance, parallel impedance is maximum.
The total line current is at a minimum at resonance.
The power factor of the circuit is unity (1.0) at resonant frequency.
Parallel resonance is often referred to as 'anti-resonance'.
High impedance at resonant frequency
Effective in band-pass and band-stop filtering
High circulating currents between L and C
Sensitive to component value variations (Q-factor dependence)
Tuned circuits in radio receivers
Oscillator circuits
Signal filtering
The formula applies to an ideal parallel LC tank circuit.
Option A (f=2╧АLCтАЛ) is incorrect as it lacks the reciprocal and inverse root relationship.
Option B (f=2╧АL/CтАЛ) is dimensionally inconsistent for frequency.
Option D (f=L/CтАЛ) is missing the frequency-determining constant factors.
C is correct тАФ The frequency at which inductive reactance equals capacitive reactance in a parallel circuit is given by f=2╧АLCтАЛ1тАЛ.
Always remember that for both series and parallel LC circuits, the resonant frequency formula is the same; however, the impedance behavior (minimum vs maximum) is opposite.