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Chapter 28: Problem 16

An AC current is given by \(I=495 \sin (9.43 t),\) with \(I\) in \(\mathrm{mA}\) and \(t\) in ms. Find (a) the rms current and (b) the frequency in \(\mathrm{Hz}\).

Short Answer

Expert verified
The RMS current is \(I_{rms} = \frac{495 \, mA}{\sqrt{2}}\) and the frequency is given by \(f = \frac{9.43}{2\pi}\) kHz

Step by step solution

01

Calculate RMS Current

The root mean square current (Irms) of a sinusoidal AC current can be calculated using the formula \(I_{rms} = \frac{I_{m}}{\sqrt{2}}\) where \(I_{m}\) is the maximum or peak current. In our case, \(I_{m} = 495mA\). So, the RMS current can be found by plugging the values into the formula: \(I_{rms} = \frac{495 \, mA}{\sqrt{2}}\)
02

Calculate the Frequency

Now, referring back to the given current equation \(I=495 \sin (9.43 t)\), the frequency of a sinusoidal function can be calculated taking the coefficient of \(t\) (in our case, 9.43 ms^-1), and equating it to \(2\pi f\). In this context, \(f\) stands for frequency. Therefore, isolating \(f\) from the equation gives us \(f = \frac{9.43}{2\pi}\), which after calculation will tell us the frequency in kilohertz.

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Most popular questions from this chapter

A power supply like that of Fig. 28.23 is supposed to deliver 22-V DC at a maximum current of 150 mA. The transformer's peak output voltage can charge the capacitor to a full \(22 \mathrm{V},\) and the primary is supplied with \(60-\mathrm{Hz}\) AC. What capacitance will ensure that the output voltage stays within \(3 \%\) of the rated \(22 \mathrm{V} ?\)

A series \(R L C\) circuit with \(R=47 \Omega, L=250 \mathrm{mH},\) and \(C=\) \(4.0 \mu \mathrm{F}\) is connected across a sine-wave generator whose peak output voltage is independent of frequency. Find the frequency range over which the peak current will exceed half its value at resonance.

Show that the unit of both capacitive and inductive reactance is the ohm.

There's an insulating gap between capacitor plates, so how can current flow in an AC circuit containing a capacitor?

An inductor and capacitor are connected in series across an AC generator, and the voltage across the inductor is higher than across the capacitor. Is the generator frequency above or below resonance?
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