Answer:
The minimum inductance needed is 2.78 H
Explanation:
Given;
frequency of the AC, f = 26.5 Hz
the root mean square voltage in the circuit, [tex]V_{rms}[/tex] = 41.2 V
the maximum current in the circuit, I₀ = 126 mA
The root mean square current is given by;
[tex]I_{rms} = \frac{I_o}{\sqrt{2} } \\\\I_{rms} = \frac{126*10^{-3}}{\sqrt{2} }\\\\I_{rms} =0.0891 \ A[/tex]
The inductive reactance is given by;
[tex]X_l = \frac{V_{rms}}{I_{rms}} \\\\X_l= \frac{41.2}{0.0891}\\\\X_l = 462.4 \ ohms[/tex]
The minimum inductance needed is given by;
[tex]X_l = \omega L\\\\X_l = 2\pi fL\\\\L = \frac{X_l}{2\pi f}\\\\L = \frac{462.4}{2\pi *26.5}\\\\L = 2.78 \ H[/tex]
Therefore, the minimum inductance needed is 2.78 H
