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Chapter 20: Problem 31

A step-down transformer has 4000 turns on the primary and 200 turns on the secondary. If the primary voltage amplitude is \(2.2 \mathrm{kV},\) what is the secondary voltage amplitude?

Short Answer

Expert verified
Answer: The secondary voltage amplitude is 0.11 kV or 110 V.

Step by step solution

01

Identify the given information

In this exercise, we are given the following information: - Primary coil turns (N1) = 4000 turns - Secondary coil turns (N2) = 200 turns - Primary voltage amplitude (V1) = 2.2 kV Our goal is to find the secondary voltage amplitude (V2).
02

Find the turns ratio

The turns ratio is the ratio between the number of turns in the primary coil to the number of turns in the secondary coil: Turns Ratio, \(k = \frac{N1}{N2}\) Plug the given values of N1 and N2 into the formula: \(k = \frac{4000}{200} = 20\)
03

Calculate the secondary voltage amplitude

Now that we have the turns ratio, we can calculate the secondary voltage amplitude V2. For transformers, the voltage ratio is equal to the turns ratio: \(k = \frac{V1}{V2}\) Rearrange the formula to find V2: \(V2 = \frac{V1}{k}\) Plug in the given primary voltage amplitude (V1 = 2.2 kV) and the turns ratio (k = 20) into the formula: \(V2 = \frac{2.2\, \text{kV}}{20}\) Calculate the secondary voltage amplitude: \(V2 = 0.11\, \text{kV}\) or \(110\, \text{V}\)
04

Write the final answer

The secondary voltage amplitude of the step-down transformer is 0.11 kV or 110 V.

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Most popular questions from this chapter

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.
A transformer with a primary coil of 1000 turns is used to step up the standard \(170-\mathrm{V}\) amplitude line voltage to a \(220-\mathrm{V}\) amplitude. How many turns are required in the secondary coil?

The armature of an ac generator is a circular coil with 50 turns and radius \(3.0 \mathrm{cm} .\) When the armature rotates at 350 rpm, the amplitude of the emf in the coil is \(17.0 \mathrm{V}\) What is the strength of the magnetic field (assumed to be uniform)?
A de motor has coils with a resistance of \(16 \Omega\) and is connected to an emf of \(120.0 \mathrm{V}\). When the motor operates at full speed, the back emf is \(72 \mathrm{V}\). (a) What is the current in the motor when it first starts up? (b) What is the current when the motor is at full speed? (c) If the current is \(4.0 \mathrm{A}\) with the motor operating at less than full speed, what is the back emf at that time?
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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