Step 1: Understanding the Concept:
In an AC circuit with a pure inductor, the opposition to the current flow is called inductive reactance (\(X_{L}\)).
The root mean square (rms) current can be calculated using Ohm's law applied to AC circuits.
Step 2: Key Formula or Approach:
The inductive reactance is found using the formula \( X_{L} = \omega L \), where \(\omega\) is the angular frequency.
The rms current is then calculated using the relation \( I_{\text{rms}} = \frac{V_{\text{rms}}}{X_{L}} \).
Step 3: Detailed Explanation:
We are given the inductance \( L = 0.1 \text{ H} \), and the rms voltage \( V_{\text{rms}} = 220 \text{ V} \).
The problem states the angular frequency is \(300 \text{ Hz}\), which indicates \(\omega = 300 \text{ rad/s}\) based on standard problem conventions despite the unit.
First, we find the inductive reactance:
\[ X_{L} = \omega L = 300 \times 0.1 = 30 \, \Omega \]
Next, we substitute this into the current formula:
\[ I_{\text{rms}} = \frac{220}{30} \]
\[ I_{\text{rms}} = \frac{22}{3} \text{ A} \]
Step 4: Final Answer:
The rms current flowing through the circuit is \(\frac{22}{3} \text{ A}\).