Question

Calculate the inductive reactance of a 3.00 mH inductor when 60.0 Hz and

10.0 kHz AC voltages are applied. (b) What is the rms current at each

frequency if the applied rms voltage is 120 V?​

Answer 1

Answer:

XL = 2πfL = 6.28(60.0/s)(3.00 mH) = 1.13 Ω at 60 Hz.

Explanation:

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Answer 2

Given:

An inductor with inductance, $L=3.00mH$

To Find:

The value of inductive reactance, $X_L$ and RMS current $I_{rms}$ by $120V$ RMS voltage at

(i) 60.0 Hz frequency

(ii) 10.0 kHz frequency

Solution:

We know that the inductive reactance of an inductor at frequency $f$ is given by

                                     $X_L=2\pi fL$

So at 60.0 Hz frequency,

                           $X_L=2\pi *60.0*3.00*10^{-3}$

                                 $=1.13$Ω

And at 10.0 kHz frequency,

                           $X_L=2\pi *10.0*10^3*3.00*10^{-3}$

                                 $=188$Ω

We can find RMS current from RMS voltage using,

                                   $I{rms}=\frac{V{rms}}{Z}$

where, $Z$ is the impedance of the circuit.

In this problem, there is no other element except the inductor. So the impedance will be equal to the inductive reactance.

                                   $Z=X_L$

So RMS current in case of 60.0 Hz frequency,

                              $I_{rms}=\frac{120}{1.13}$

                                      $=106A$

In the case of 10.0 kHz frequency,

                              $I_{rms}=\frac{120}{188}$

                                      $=0.64A$

Hence the inductive reactance and RMS current in the case of 60.0 Hz frequency are 1.13Ω and 106A and in the case of 10.0 kHz frequency are 188Ω and 0.64A.