Question

An inductor is connected to a 18 kHz oscillator. The peak current is 70 mA when the rms voltage is 5.4 V What is the value of the inductance L

Answer 1

Answer:

The value of the inductance is 0.955 mH

Explanation:

Given;

frequency of the oscillator, f = 18 kHz = 18,000 Hz

the peak current, I₀ = 70 mA = 0.07 A

the root mean square voltage, $V_{rms}$ = 5.4 V

The root mean square current is given as;

$I_{rms}= \frac{I_o}{\sqrt{2} }$

$I_{rms} = \frac{0.07}{\sqrt{2} } \\\\I_{rms} = 0.05 \ A$

Inductive reactance is given by;

$X_L =\frac{V_{rms}}{I_{rms}} \\\\X_L = \frac{5.4}{0.05} \\\\X_L = 108 \ ohms$

Inductance is given by;

$L = \frac{X_L}{2\pi f} \\\\L = \frac{108}{2\pi *18,000} \\\\L = 9.55 *10^{-4} \ H$

L = 0.955 mH

Therefore, the value of the inductance is 0.955 mH