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Ch. 29 - Electromagnetic Induction and Faraday's Law
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook
All textbooksGiancoli Douglas 5th editionCh. 29 - Electromagnetic Induction and Faraday's LawProblem 48
Chapter 28, Problem 48

A model-train transformer plugs into 120-V ac and draws 0.35 A while supplying 6.5 A to the train.
(a) What voltage is present across the tracks?
(b) Is the transformer step-up or step-down?

Verified step by step guidance
1
Step 1: Use the principle of conservation of power for an ideal transformer. The input power (primary side) is equal to the output power (secondary side). The formula is: Pin = Pout, where P = V × I (voltage times current).
Step 2: Calculate the output voltage across the tracks using the formula: Vout = Vin × (Iin / Iout). Substitute the given values: Vin = 120 V, Iin = 0.35 A, and Iout = 6.5 A.
Step 3: Simplify the ratio (Iin / Iout) and multiply it by Vin to find Vout. This will give the voltage across the tracks.
Step 4: Determine whether the transformer is step-up or step-down by comparing the input voltage (Vin) to the output voltage (Vout). If Vout < Vin, it is a step-down transformer; otherwise, it is step-up.
Step 5: Conclude the solution by stating the calculated output voltage and whether the transformer is step-up or step-down based on the comparison in Step 4.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ohm's Law

Ohm's Law states that the current (I) flowing through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R) of the conductor. This relationship is expressed as V = I × R. Understanding this law is crucial for analyzing electrical circuits, including transformers, as it helps determine the voltage and current relationships.
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Transformer Basics

A transformer is an electrical device that transfers electrical energy between two or more circuits through electromagnetic induction. It consists of primary and secondary coils, and its operation is based on the principle that a changing current in the primary coil creates a changing magnetic field, inducing a voltage in the secondary coil. The voltage ratio between the primary and secondary coils determines whether the transformer is a step-up or step-down transformer.
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Power Conservation in Transformers

In an ideal transformer, the power input to the primary coil equals the power output from the secondary coil, expressed as P_primary = P_secondary. This means that the product of voltage and current remains constant, allowing for the calculation of unknown voltages or currents. This principle is essential for solving the given problem, as it helps determine the voltage across the tracks based on the current supplied to the train.
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Related Practice
Textbook Question

Neon signs require 12 kV for their operation. To operate from a 240-V line, what must be the ratio of secondary to primary turns of the transformer? What would the voltage output be if the transformer were connected in reverse?

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Textbook Question

If 75 MW of power at 45 kV (rms) arrives at a town from a generator via transmission lines of total resistance 3.0 Ω, calculate (a) the emf at the generator end of the lines, and (b) the fraction of the power generated that is wasted in the lines.

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Textbook Question

(II) For the electric power transmission system shown in Fig. 29–26, what is the ratio Ns/Np for (a) the step-up transformer, (b) the step-down transformer next to the home?

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Textbook Question

(III) In a circular region, there is a uniform magnetic field B→\(\overrightarrow{B}\) pointing into the page (Fig. 29–56). An xy coordinate system has its origin at the circular region’s center. A free positive point charge +Q = 1.0 μC is initially at rest at a position x = +10 cm on the x axis. If the magnitude of the magnetic field is now decreased at a rate of -0.10 T/s, what force (magnitude and direction) will act on +Q?


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Textbook Question

A transformer has 680 turns in the primary coil and 85 in the secondary coil. What kind of transformer is this, and by what factor does it change the voltage? By what factor does it change the current?

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