Which of the following statements is true with reference to an L-C resonant circuit?
(1) The impedance of a parallel L-C circuit is low at resonance and higher at frequencies
above and below resonance. The impedance of a series circuit is high at resonance and
low at frequencies above and below resonance.
(2) The impedance of a parallel L-C circuit is high at resonance and lower at frequencies
above and below resonance. The impedance of a series circuit is low at resonance and
higher at frequencies above and below resonance.
(3) At resonance any L-C circuit exhibits lower impedance than at frequencies above
and below the resonant frequency.
(4) At resonance any L-C circuit exhibits higher impedance than at frequencies above
and below the resonant frequency.
Parallel:
impedance ----> infinity at resonance
Series
impedance ----> 0 at resonance (in reality to R because there is always some resistance)
1. FALSE: The impedance is max at resonance and min at frequencies above and below resonance. The impedance of a series resonant circuit is min at resonance and max at frequencies above and below resonance.
2. TRUE.
3. FALSE: The statement is true for the series resonant circuit only.
4. FALSE: The statement is true for the parallel resonant circuit only.
The correct statement is:
(2) The impedance of a parallel L-C circuit is high at resonance and lower at frequencies above and below resonance. The impedance of a series circuit is low at resonance and higher at frequencies above and below resonance.
At resonance, an L-C circuit exhibits the minimum impedance in a parallel circuit, making it easier for current to flow through. In a series circuit, the impedance is maximum at resonance, resulting in a higher voltage drop across the circuit. Hence, statement (2) is true with reference to an L-C resonant circuit.
To determine which statement is true, we need to understand the behavior of an L-C resonant circuit at resonance.
An L-C resonant circuit consists of an inductor (L) and a capacitor (C) connected either in series or in parallel. The resonant frequency of the circuit is the frequency at which the inductive and capacitive reactances cancel each other out, resulting in a purely resistive impedance.
Let's go through each statement and analyze its accuracy:
(1) The impedance of a parallel L-C circuit is low at resonance and higher at frequencies above and below resonance. The impedance of a series circuit is high at resonance and low at frequencies above and below resonance.
This statement is incorrect. In a parallel L-C circuit, the impedance is high at resonance and lower at frequencies above and below resonance. In a series L-C circuit, the impedance is low at resonance and higher at frequencies above and below resonance.
(2) The impedance of a parallel L-C circuit is high at resonance and lower at frequencies above and below resonance. The impedance of a series circuit is low at resonance and higher at frequencies above and below resonance.
This statement is also incorrect. The correct explanation is the opposite of statement (2). The impedance of a parallel L-C circuit is low at resonance and higher at frequencies above and below resonance. The impedance of a series circuit is high at resonance and lower at frequencies above and below resonance.
(3) At resonance, any L-C circuit exhibits lower impedance than at frequencies above and below the resonant frequency.
This statement is incorrect. The impedance of a parallel L-C circuit is not lower at resonance compared to frequencies above and below resonance. The impedance may be lower compared to other frequencies in the circuit, but not necessarily at resonance.
(4) At resonance, any L-C circuit exhibits higher impedance than at frequencies above and below the resonant frequency.
This statement is correct. At resonance, both parallel and series L-C circuits exhibit a higher impedance compared to frequencies above and below the resonant frequency. This is due to the cancelation of inductive and capacitive reactances, resulting in a purely resistive impedance.
Therefore, the correct statement is (4) - At resonance, any L-C circuit exhibits higher impedance than at frequencies above and below the resonant frequency.