Ch. 29 - Electromagnetic Induction and Faraday's Law

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179당신이 사용하는 게 아니라요?교과서 변경

Giancoli Douglas 5th edition

Ch. 29 - Electromagnetic Induction and Faraday's Law

문제 46

28장, 문제 46

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?

검증된 단계별 안내

Identify the type of transformer by comparing the number of turns in the primary coil (Nₚ = 680) and the secondary coil (Nₛ = 85). Since Nₚ > Nₛ, this is a step-down transformer.

Use the turns ratio formula to determine the voltage change factor: $ \text{Voltage Ratio} = \frac{Nₚ}{Nₛ} $. Substitute $ Nₚ = 680 $ and $ Nₛ = 85 $ into the formula.

Recognize that the current in a transformer is inversely proportional to the voltage. Use the current ratio formula: $ \text{Current Ratio} = \frac{Nₛ}{Nₚ} $. Substitute $ Nₛ = 85 $ and $ Nₚ = 680 $ into the formula.

Conclude that the transformer decreases the voltage by the factor calculated in step 2 and increases the current by the factor calculated in step 3.

Verify the conservation of power principle: $ P_{\text{primary}} = P_{\text{secondary}} $, where $ P = V \cdot I $, to ensure the calculations align with the physical behavior of transformers.

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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, where the primary coil receives input voltage and the secondary coil delivers output voltage. The ratio of the number of turns in the coils determines whether the transformer steps up or steps down the voltage.

Turns Ratio

The turns ratio of a transformer is the ratio of the number of turns in the primary coil to the number of turns in the secondary coil. It is crucial for determining how the voltage and current change between the primary and secondary sides. For a transformer with 'N1' turns in the primary and 'N2' turns in the secondary, the voltage change factor is given by V2/V1 = N2/N1, and the current change factor is I2/I1 = N1/N2.

Voltage and Current Transformation

In a transformer, when the voltage is stepped up (increased), the current is stepped down (decreased), and vice versa. This relationship is governed by the conservation of energy principle, which states that the power input to the primary coil (P1 = V1 * I1) must equal the power output from the secondary coil (P2 = V2 * I2), assuming no losses. Thus, the product of voltage and current remains constant across the transformer.

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(III) Suppose a conducting rod (mass m, resistance R) rests on two frictionless and resistanceless parallel rails a distance ℓ apart in a uniform magnetic field $\vec{B}$ (⊥ to the rails and to the rod) as in Fig. 29–53. At t = 0, the rod is at rest and a source of emf is connected to the points a and b. Determine the speed of the rod as a function of time if (a) the source puts out a constant current I, (b) the source puts out a constant emf ε₀. (c) Does the rod reach a terminal speed in either case? If so, what is it?

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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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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?

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교과서 질문

(II) A conducting rod rests on two long frictionless parallel rails in a magnetic field $\vec{B}$ (⊥ to the rails and rod) as in Fig. 29–53. (a) If the rails are horizontal and the rod is given an initial push, will the rod travel at constant speed even though a magnetic field is present? (b) Suppose at t = 0, when the rod has speed v = v₀, the two rails are connected electrically by a wire from point a to point b. Assuming the rod has resistance R and the rails have negligible resistance, determine the speed of the rod as a function of time. Discuss your answer.

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