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Answer :
Final Answer:
Assertion : In series LCR circuit resonance can take place.
Reason : Resonance takes place if inductance and capacitive resistances are equal and opposite. The above mentioned both Assertion and Reason are true but Reason is not the correct explanation for Assertion. Option b
Explanation:
In a series LCR circuit, resonance occurs when the inductive reactance (X_L) and capacitive reactance (X_C) are equal in magnitude but opposite in phase. However, the given reason states that resonance takes place if inductance and capacitive resistances are equal and opposite, which is not accurate. Resonance in an LCR circuit is based on reactances, not resistances. Therefore, while both the assertion and reason are true, the reason does not correctly explain the assertion.
Resonance is achieved when X_L = X_C. The inductive reactance (X_L) is given by the formula X_L = 2πfL, where 'f' is the frequency and 'L' is the inductance. The capacitive reactance (X_C) is given by the formula X_C = 1 / (2πfC), where 'C' is the capacitance. At resonance, these two reactances are equal, leading to cancellation and maximum current flow.
The reason provided seems to confuse resistances with reactances. Resistances are associated with energy dissipation, while reactances deal with the opposition to the change in current flow. Therefore, in the context of resonance in LCR circuits, the correct comparison is between inductive and capacitive reactances, not resistances. Hence, option B is the appropriate choice, as both the assertion and reason are true, but the reason does not accurately explain the assertion. (Option B)
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Rewritten by : Brahmana