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Chapter 20: Problem 8

The armature of an ac generator is a rectangular coil \(2.0 \mathrm{cm}\) by \(6.0 \mathrm{cm}\) with 80 turns. It is immersed in a uniform magnetic field of magnitude 0.45 T. If the amplitude of the emf in the coil is $17.0 \mathrm{V},$ at what angular speed is the armature rotating?

Short Answer

Expert verified
Answer: The angular speed of the rectangular coil is approximately \(393.52\ \mathrm{rad/s}\).

Step by step solution

01

Write down the formula

We use the formula for the amplitude of the emf in a rotating coil: \(emf = NBA\omega\sin{\omega t}\). Since we are given the amplitude of the emf, we can set \(emf = NBA\omega\).
02

Substitute the given values

We are given the following values: \(emf = 17.0\ \mathrm{V}\) \(N = 80\) turns \(B = 0.45\ \mathrm{T}\) \(A = 2.0\,\mathrm{cm} \times 6.0\,\mathrm{cm} = 12.0\,\mathrm{cm}^2 = 0.0012\,\mathrm{m}^2\) Now we can plug these values into the equation: \(17.0\ \mathrm{V} = (80)(0.45 \mathrm{T})(0.0012\ \mathrm{m}^2)\omega\)
03

Solve for the angular speed \(\omega\)

Now we solve for \(\omega\): $$ \omega = \frac{17.0\ \mathrm{V}}{(80)(0.45 \mathrm{T})(0.0012\ \mathrm{m}^2)} = \frac{17.0}{0.0432} \mathrm{rad/s} $$ $$ \omega \approx 393.52\ \mathrm{rad/s} $$
04

Write the final answer

The angular speed at which the armature rotating is approximately \(393.52\ \mathrm{rad/s}\).

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Most popular questions from this chapter

A TV tube requires a 20.0 -kV-amplitude power supply. (a) What is the turns ratio of the transformer that raises the 170 -V-amplitude household voltage to \(20.0 \mathrm{kV} ?\) (b) If the tube draws 82 W of power, find the currents in the primary and secondary windings. Assume an ideal transformer.
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 \(B ?\)
A horizontal desk surface measures \(1.3 \mathrm{m} \times 1.0 \mathrm{m} .\) If Earth's magnetic field has magnitude \(0.44 \mathrm{mT}\) and is directed \(65^{\circ}\) below the horizontal, what is the magnetic flux through the desk surface?
A transformer for an answering machine takes an ac voltage of amplitude $170 \mathrm{V}\( as its input and supplies a \)7.8-\mathrm{V}$ amplitude to the answering machine. The primary has 300 turns. (a) How many turns does the secondary have? (b) When idle, the answering machine uses a maximum power of \(5.0 \mathrm{W}\). What is the amplitude of the current drawn from the 170 -V line?
A transformer with 1800 turns on the primary and 300 turns on the secondary is used in an electric slot car racing set to reduce the input voltage amplitude of \(170 \mathrm{V}\) from the wall output. The current in the secondary coil is of amplitude \(3.2 \mathrm{A}\). What is the voltage amplitude across the secondary coil and the current amplitude in the primary coil?
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