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ANSWER

To determine whether the current leads or lags the voltage and by what angle, we need to calculate the phase difference between them.

The impedance of the series RLC circuit is given by:

\[

Z = \sqrt{R^2 + (X_L - X_C)^2}

\]

Where

\[

X_L = 2πfL = 2π(50)(0.1) = 31.42 Ω

\]

\[

X_C = \frac{1}{{2πfC}} = \frac{1}{{2π(50)(30 \times 10^{-6})}} = 106.1 Ω

\]

Substituting these values into the equation, we get:

\[

Z = \sqrt{(200)^2 + (31.42 - 106.1)^2} = \sqrt{40,000 + (-74.68)^2} = \sqrt{40,000 + 5,572.09} = \sqrt{45,572.09} = 213.67 Ω

\]

The phase angle can be calculated using the tangent inverse of the reactance difference divided by the resistance:

\[

\theta = \tan^{-1}\left(\frac{{X_L - X_C}}{{R}}\right) = \tan^{-1}\left(\frac{{31.42 - 106.1}}{{200}}\right) = \tan^{-1}\left(-0.3729\right) = -20.19°

\]

Since the angle is negative, the current lags the voltage by 20.19°.