Physics: An inductor is connected to a 26.5 Hz power supply that produces a 41.2 V rms voltage. What minimum inductance is needed to keep the maximum current in the circuit below 126 mA?

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An inductor is connected to a 26.5 Hz power supply

varonadestiny1109

08.02.2022

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, $V_{rms}$ = 41.2 V

the maximum current in the circuit, I₀ = 126 mA

The root mean square current is given by;

$I_{rms} = \frac{I_o}{\sqrt{2} } \\\\I_{rms} = \frac{126*10^{-3}}{\sqrt{2} }\\\\I_{rms} =0.0891 \ A$

The inductive reactance is given by;

$X_l = \frac{V_{rms}}{I_{rms}} \\\\X_l= \frac{41.2}{0.0891}\\\\X_l = 462.4 \ ohms$

The minimum inductance needed is given by;

$X_l = \omega L\\\\X_l = 2\pi fL\\\\L = \frac{X_l}{2\pi f}\\\\L = \frac{462.4}{2\pi *26.5}\\\\L = 2.78 \ H$

Therefore, the minimum inductance needed is 2.78 H

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