The total reactance of the inductor and the capacitor is 470.1 ohms.
The given parameters;
The inductive reactance of the coil is calculated as follows;
[tex]X_l = \omega L\\\\X_l = 2\pi f L\\\\X_l = 2\pi \times 60 \times 250 \times 10^{-3}\\\\X_l = 94.26 \ ohms[/tex]
The capacitive reactance of the capacitor is calculated as follows;
[tex]X_c = \frac{1}{\omega C} \\\\X_c = \frac{1}{2\pi f C} \\\\X_c = \frac{1}{2\pi \times 60 \times 4.7 \times 10^{-6}} \\\\X_c = 564.31 \ ohms[/tex]
The impedance of the circuit is calculated as follows;
[tex]Z = \sqrt{(X_c - X_l)^2} \\\\Z = X_c - X_l\\\\Z = 564.31 - 94.26\\\\Z = 470.1 \ ohms[/tex]
Thus, the total reactance of the inductor and the capacitor is 470.1 ohms.
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