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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 de motor is connected to a constant emf of \(12.0 \mathrm{V}\) The resistance of its windings is \(2.0 \Omega .\) At normal operating speed, the motor delivers \(6.0 \mathrm{W}\) of mechanical power. (a) What is the initial current drawn by the motor when it is first started up? (b) What current does it draw at normal operating speed? (c) What is the back emf induced in the windings at normal speed?
The magnetic field between the poles of an electromagnet is \(2.6 \mathrm{T} .\) A coil of wire is placed in this region so that the field is parallel to the axis of the coil. The coil has electrical resistance \(25 \Omega,\) radius $1.8 \mathrm{cm},\( and length \)12.0 \mathrm{cm} .$ When the current supply to the electromagnet is shut off, the total charge that flows through the coil is \(9.0 \mathrm{mC} .\) How many turns are there in the coil?
In this problem, you derive the expression for the self inductance of a long solenoid [Eq. \((20-15 a)] .\) The solenoid has \(n\) turns per unit length, length \(\ell,\) and radius \(r\) Assume that the current flowing in the solenoid is \(I\) (a) Write an expression for the magnetic field inside the solenoid in terms of \(n, \ell, r, I,\) and universal constants. (b) Assume that all of the field lines cut through each turn of the solenoid. In other words, assume the field is uniform right out to the ends of the solenoid-a good approximation if the solenoid is tightly wound and sufficiently long. Write an expression for the magnetic flux through one turn. (c) What is the total flux linkage through all turns of the solenoid? (d) Use the definition of self-inductance [Eq. \((20-14)]\) to find the self inductance of the solenoid.
Tim is using a cordless electric weed trimmer with a de motor to cut the long weeds in his back yard. The trimmer generates a back emf of \(18.00 \mathrm{V}\) when it is connected to an emf of \(24.0 \mathrm{V}\) de. The total electrical resistance of the electric motor is \(8.00 \Omega .\) (a) How much current flows through the motor when it is running smoothly? (b) Suddenly the string of the trimmer gets wrapped around a pole in the ground and the motor quits spinning. What is the current through the motor when there is no back emf? What should Tim do?
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.
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