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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 (蠅) is: E = k * 蠅 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 * 蠅_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

A flip coil is a device used to measure a magnetic field. A coil of radius $r, N\( turns, and electrical resistance \)R$ is initially perpendicular to a magnetic field of magnitude B. The coil is connected to a special kind of galvanometer that measures the total charge \(Q\) that flows through it. To measure the field, the flip coil is rapidly flipped upside down. (a) What is the change in magnetic flux through the coil in one flip? (b) If the time interval during which the coil is flipped is \(\Delta t,\) what is the average induced emf in the coil? (c) What is the average current that flows through the galvanometer? (d) What is the total charge \(Q\) in terms of \(r, N, R,\) and \(B ?\)
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