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In the given circuit, the rms value of current $$(I_{rms})$$ through the resistor $$R$$ is:
Net Reactance $$X = X_L - X_C$$
Total Impedance $$Z = \sqrt{R^2 + (X_L - X_C)^2}$$
$$X = 200\ \Omega - 100\ \Omega = 100\ \Omega$$
$$Z = \sqrt{100^2 + 100^2} = 100\sqrt{2}\ \Omega$$
$$I_{\text{rms}} = \frac{V_{\text{rms}}}{Z}$$
$$I_{\text{rms}} = \frac{200\sqrt{2}\ \text{V}}{100\sqrt{2}\ \Omega}$$
$$I_{\text{rms}} = 2\ \text{A}$$
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