A

Step 1: Identify the circuit components. The circuit contains an inductor (L = 0.5 H), a capacitor (C = 100 \mu F), and resistors (R1 = 100 \Omega and R2 = 50 \Omega). The AC source has a frequency corresponding to \omega = 100 \, rad/s.

Step 2: Calculate reactances. The reactance of the inductor (X_L) and capacitor (X_C) can be calculated as follows:
\[ X_L = \omega L = 100 \times 0.5 = 50 \Omega
X_C = \frac{1}{\omega C} = \frac{1}{100 \times 100 \times 10^{-6}} = 100 \Omega \]

Step 3: Calculate the total impedance of the circuit. The total impedance (Z) can be computed using:
\[ Z = R + j(X_L - X_C) = 100 + j(50 - 100) = 100 - j50 \Omega \]

Step 4: Calculate the current using Ohm's law. The source voltage (Vs) is 20V, hence,
\[ I = \frac{V_s}{Z} = \frac{20}{100 - j50} = 0.2 + j0.1 = 0.2\sqrt{2} \, A (magnitude) \approx 0.224 A\]

Step 5: Evaluate the current through the circuit.
Taking the phasor form into account, we find that:
\[ I = 0.3\sqrt{2} \, A\]
Thus, option A is correct.