In a series LCR circuit, a resistor of 300 $\mathrm{\Omega }$, 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 _____ × 10⁴ radians s^–1.

For maximum current in a series LCR circuit, the resonance condition must be satisfied. The resonant angular frequency $\omega_0$ is given by:

$$\omega_0 = \frac{1}{\sqrt{LC}}$$

Step 1: Given Data

Resistance $R = 300 \Omega$ (not needed for resonance frequency calculation),

Capacitance $C = 25$ nF $= 25 \times 10^{-9}$ F,

Inductance $L = 100$ mH $= 100 \times 10^{-3}$ H.

Step 2: Calculate Resonant Angular Frequency $\omega_0$

$$\omega_0 = \frac{1}{\sqrt{L C}}$$

Substituting the values:

$$\omega_0 = \frac{1}{\sqrt{(100 \times 10^{-3}) \times (25 \times 10^{-9})}}$$

 $=\frac{1}{\sqrt{2500}\times {10}^{-6}}$ $=\frac{{10}^6}{50}=2\times {10}^4 \mathrm{rad}/\mathrm{s}$

 ${\omega }_0=2\times {10}^4 \mathrm{rad}/\mathrm{s}$ 

Final Answer:

$2$