Answer:
The resistance of the inductor at resonance is 258.76 ohms.
Explanation:
Given;
resistance of the resistor, R = 305 ohm
capacitance of the capacitor, C = 1.1 μF = 1.1 x 10⁻⁶ F
inductance of the inductor, L = 42 mH = 42 x 10⁻³ H = 0.042 H
At resonance the inductive reactance is equal to capacitive reactance.
[tex]\omega L = \frac{1}{\omega C}\\\\2\pi F_0 L = \frac{1}{2\pi F_0 C}\\\\F_0 = \frac{1}{2\pi\sqrt{LC} }[/tex]
Where;
F₀ is the resonance frequency
[tex]F_0 = \frac{1}{2\pi\sqrt{LC} } \\\\F_0 = \frac{1}{2\pi\sqrt{(0.024)(1.1*10^{-6})} }\\\\F_0 =980.4 \ Hz[/tex]
The inductive reactance is given by;
[tex]X_l = 2\pi F_0 L\\\\X_l = 2\pi (980.4)(0.042) \\\\X_l = 258.76 \ ohms[/tex]
Therefore, the resistance of the inductor at resonance is 258.76 ohms.
