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Chapter 28: Problem 23

A \(50-\mathrm{mH}\) inductor is connected across a \(10-\mathrm{V}\) rms AC generator, and a 2.0 -mA rms current flows. What's the generator frequency?

Short Answer

Expert verified
Use steps 1 through 4 to calculate the generator frequency. Solve the equation in step 3 to get the generator frequency.

Step by step solution

01

Identify the relevant formulas

The voltage across an inductor in an AC circuit can be found using the formula \(V = I * 2 * \π * f * L\), where \(V\) is voltage, \(I\) is current, \(f\) is the frequency of the generator, and \(L\) is the inductance of the inductor. In this case, we want to solve for \(f\), so we need to rearrange the equation to give us: \(f = V / (I * 2 * \π * L)\).
02

Convert values to standard SI units

The given values are \(V = 10 V\), \(I = 2.0 mA\) and \(L = 50 mH\). We need to convert the current from mA to A by multiplying by \(10^-3\), and inductance from mH to H by multiplying by \(10^-3\). This gives us \(I = 2.0 \times 10^-3 A\) and \(L = 50 \times 10^-3 H\).
03

Substituting the given values into the rearranged formula

Now, we substitute the given values into the formula: \(f = 10 / ((2.0 \times 10^-3 A) * 2 * \π * (50 \times 10^-3 H))\)
04

Solving for the frequency

After solving the expression above, we should get the generator frequency \(f\)

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Most popular questions from this chapter

A \(470-\Omega\) resistor, \(10-\mu \mathrm{F}\) capacitor, and \(750-\mathrm{mH}\) inductor are each connected across \(6.3-\mathrm{V}\) rms, \(60-\mathrm{Hz}\) AC power. Find the rms current in each.

For safety, medical equipment connected to patients is often powered by an isolation transformer, whose primary is connected to 120 -V AC power and whose secondary delivers \(120-\mathrm{V}\) power. What's the turns ratio of such a transformer?

A series \(R L C\) circuit has power factor 0.80 and impedance \(100 \Omega\) at \(60 \mathrm{Hz}\). (a) What's the resistance? (b) If the inductance is \(0.10 \mathrm{H},\) what's the resonant frequency?

A series \(R L C\) circuit has \(R=18 \mathrm{k} \Omega, L=20 \mathrm{mH},\) and resonates at \(4.0 \mathrm{kHz}\). (a) What's the capacitance? (b) Find the circuit's impedance at resonance and (c) at \(3.0 \mathrm{kHz}\)

The FM radio band covers the frequency range \(88-108\) MHz. If the variable capacitor in an FM receiver ranges from \(10.9 \mathrm{pF}\) to \(16.4 \mathrm{pF},\) what inductor should be used to make an \(L C\) circuit whose resonant frequency spans the FM band?
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