In a series LCR circuit, a resistor of 300Ω, a capacitor of 25 nF and an inductor of 100 mH are used. For maximum current in the circuit, the angular frequency of the ac source is _____$$\times 10^{4}\text{ radians }s^{-1}$$

For a series LCR circuit, the current in the circuit is maximum at the resonant frequency. This condition occurs when the inductive reactance is exactly equal to the capacitive reactance:

$$ X_L = X_C $$

$$ \omega L = \frac{1}{\omega C} $$

From this, the resonant angular frequency $$\omega$$ is given by the formula:

$$ \omega = \frac{1}{\sqrt{LC}} $$

$$ \omega = \frac{1}{\sqrt{10^{-1} \times 25 \times 10^{-9}}} $$

$$ \omega = \frac{1}{\sqrt{25 \times 10^{-10}}} $$

$$ \omega = \frac{1}{5 \times 10^{-5}} $$

$$ \omega = 2 \times 10^4 \text{ rad s}^{-1} $$