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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: 9780137488179Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoGiancoli Douglas 5th editionCh. 29 - Electromagnetic Induction and Faraday's LawProblema 46
Capitolo 28, Problema 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?

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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.
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Transformers

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.
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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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