LR, RC and LCR Circuits: Practice Problem & Solution
Assertion (A): The impedance of series L-C-R circuit can be greater, equal or less than the resistance. Reason (R): The minimum impedance of series LCR circuit depends over angular frequency of applied emf.
Solution Explained:
To solve this problem, we apply the core principles of LR, RC and LCR Circuits. Understanding the underlying formula is key to arriving at the correct answer below:
The impedance of a series \(LCR\) circuit is given by \(Z = \sqrt{R^2 + (X_L - X_C)^2}\). Since \((X_L - X_C)^2\) is always non-negative, \(Z\) is always greater than or equal to \(R\). Thus, (A) is false. The minimum impedance occurs at resonance, where \(Z_{min} = R\). This minimum value depends only on \(R\) and not on the angular frequency \(omega\). Thus, (R) is also false.
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