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Chapter 20: Problem 6

When the armature of an ac generator rotates at $15.0 \mathrm{rad} / \mathrm{s},\( the amplitude of the induced emf is \)27.0 \mathrm{V}$ What is the amplitude of the induced emf when the armature rotates at $10.0 \mathrm{rad} / \mathrm{s} ?$ (tutorial: generator)

Short Answer

Expert verified
Answer: The amplitude of the induced EMF when the armature rotates at 10 rad/s is 18 V.

Step by step solution

01

Understand the relationship between induced EMF and angular velocity

The induced EMF in an AC generator is directly proportional to the angular velocity of the armature. The equation that relates the induced EMF (E) and the angular velocity (ω) is: E = k * ω where k is the proportionality constant.
02

Calculate the proportionality constant k

Plugging the given values for induced EMF (27 V) and angular velocity (15 rad/s) into the equation from Step 1, we can solve for the proportionality constant k: 27 = k * 15 k = \frac{27}{15} = 1.8
03

Calculate the amplitude of the induced EMF for the new angular velocity

Now that we have the proportionality constant k (1.8), we can use it to find the amplitude of the induced EMF when the armature rotates at 10 rad/s: E_new = k * ω_new E_new = 1.8 * 10 E_new = 18 So, the amplitude of the induced EMF when the armature rotates at 10 rad/s is 18 V.

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Most popular questions from this chapter

Calculate the equivalent inductance \(L_{\mathrm{eq}}\) of two ideal inductors, \(L_{1}\) and \(L_{2},\) connected in series in a circuit. Assume that their mutual inductance is negligible. [Hint: Imagine replacing the two inductors with a single equivalent inductor \(L_{\mathrm{cq}} .\) How is the emf in the series equivalent related to the emfs in the two inductors? What about the currents?]
A \(0.30-\mathrm{H}\) inductor and a \(200.0-\Omega\) resistor are connected in series to a \(9.0-\mathrm{V}\) battery. (a) What is the maximum current that flows in the circuit? (b) How long after connecting the battery does the current reach half its maximum value? (c) When the current is half its maximum value, find the energy stored in the inductor, the rate at which energy is being stored in the inductor, and the rate at which energy is dissipated in the resistor. (d) Redo parts (a) and (b) if, instead of being negligibly small, the internal resistances of the inductor and battery are \(75 \Omega\) and \(20.0 \Omega\) respectively.
The primary coil of a transformer has 250 turns; the secondary coil has 1000 turns. An alternating current is sent through the primary coil. The emf in the primary is of amplitude \(16 \mathrm{V}\). What is the emf amplitude in the secondary? (tutorial: transformer)
(a) For a particle moving in simple harmonic motion, the position can be written \(x(t)=x_{\mathrm{m}}\) cos \(\omega t .\) What is the velocity \(v_{x}(t)\) as a function of time for this particle? (b) Using the small-angle approximation for the sine function, find the slope of the graph of \(\Phi(t)=\Phi_{0} \sin \omega t\) at \(t=0 .\) Does your result agree with the value of \(\Delta \Phi / \Delta t=\omega \Phi_{0} \cos \omega t\) at \(t=0 ?\)
The time constant \(\tau\) for an \(L R\) circuit must be some combination of $L, R,\( and \)\mathscr{E} .$ (a) Write the units of each of these three quantities in terms of \(\mathrm{V}, \mathrm{A},\) and \(\mathrm{s}\) (b) Show that the only combination that has units of seconds is \(L / R\)
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