#### Question

In a series LCR circuit, obtain the condition under which the impedance of the circuit is minimum ?

#### Solution

(i) The impedance of a series LCR circuit is given by

\[Z = \sqrt{R^2 + \left( \omega L - \frac{1}{\omega C} \right)^2}\]

Z will be minimum when \[\omega L = \frac{1}{\omega C}\]

i.e., when the circuit is under resonance. Hence, for this condition, Z will be minimum and will be equal to R.

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Solution In a Series Lcr Circuit, Obtain the Condition Under Which the Impedance of the Circuit is Minimum ? Concept: Ac Voltage Applied to a Series Lcr Circuit.