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Chapter 20: Problem 34

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)

Short Answer

Expert verified
Answer: 64V

Step by step solution

01

Identify the transformer equation.

The transformer equation is given by: \(\frac{V_p}{V_s} = \frac{N_p}{N_s}\) where \(V_p\) is the emf amplitude in the primary coil, \(V_s\) is the emf amplitude in the secondary coil, \(N_p\) is the number of turns in the primary coil, and \(N_s\) is the number of turns in the secondary coil.
02

Plug in the given values.

We are given \(N_p = 250\) turns, \(N_s = 1000\) turns, and \(V_p = 16 \mathrm{V}\). Substituting these values into the transformer equation, we get: \(\frac{16}{V_s} = \frac{250}{1000}\)
03

Solve for \(V_s\).

To solve for \(V_s\), we can cross-multiply and simplify: \(16 \times 1000 = V_s \times 250\) \(16000 = 250V_s\) Now, divide both sides by 250: \(V_s = \frac{16000}{250}\)
04

Calculate the emf amplitude in the secondary coil.

After the division, we get the emf amplitude in the secondary coil: \(V_s = 64 \mathrm{V}\) Therefore, the emf amplitude in the secondary coil is \(64 \mathrm{V}\).

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Most popular questions from this chapter

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 100 -turn coil with a radius of \(10.0 \mathrm{cm}\) is mounted so the coil's axis can be oriented in any horizontal direction. Initially the axis is oriented so the magnetic flux from Earth's field is maximized. If the coil's axis is rotated through \(90.0^{\circ}\) in \(0.080 \mathrm{s},\) an emf of $0.687 \mathrm{mV}$ is induced in the coil. (a) What is the magnitude of the horizontal component of Earth's magnetic field at this location? (b) If the coil is moved to another place on Earth and the measurement is repeated, will the result be the same?
How much energy due to Earth's magnetic field is present in $1.0 \mathrm{m}^{3}$ of space near Earth's surface, at a place where the field has magnitude \(0.45 \mathrm{mT} ?\)
An ideal inductor of inductance \(L\) is connected to an ac power supply, which provides an emf \(\mathscr{E}(t)=\mathscr{E}_{\mathrm{m}}\) sin \(\omega t\) (a) Write an expression for the current in the inductor as a function of time. [Hint: See Eq. \((20-7) .]\) (b) What is the ratio of the maximum emf to the maximum current? This ratio is called the reactance. (c) Do the maximum emf and maximum current occur at the same time? If not, how much time separates them?
A \(0.67 \mathrm{mH}\) inductor and a \(130 \Omega\) resistor are placed in series with a \(24 \mathrm{V}\) battery. (a) How long will it take for the current to reach \(67 \%\) of its maximum value? (b) What is the maximum energy stored in the inductor? (c) How long will it take for the energy stored in the inductor to reach \(67 \%\) of its maximum value? Comment on how this compares with the answer in part (a).
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