Detailed explanation would be much appreciated Purely Inductive AC Circuit In a

Question

Detailed explanation would be much appreciated

Purely Inductive AC Circuit In a purely inductive AC circuit, L = 27.0 mH and the rms voltage is 220 V. Calculate the inductive reactance and rms current in the circuit if the frequency is 60.0 Hz. Conceptualize The figure shows the physical situation for this problem Categorize We evaluate the reactance and the current from equations developed in this section, so we categorize this example as a substitution problem. Use the following equation to find the inductive reactance: Use an rms version of the equation for the maximum current in an inductor to find the rms current: What if the frequency is now 250 Hz, and the maximum voltage (not rms) is 220 V? Find the rms current in the circuit. Follow the example closely. What is the rms voltage flow? Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error.

Explanation / Answer

dVrms = Vmax / [2]1/2

we know that

Irms = dVrms / 2 * pi * f * L

= 0.7071 Vmax / 2 * pi * f * L

Now substitute values and solve for Irms

Irms = 0.7071 * 220 / 2 * 3.14 * 250 * 27 x 10-3

= 3.6697 A

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