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 44

28장, 문제 44

A transformer is designed to change 117 V into 13,500 V, and there are 172 turns in the primary coil. How many turns are in the secondary coil?

Name: Physics for Scientists and Engineers
Author: Giancoli Douglas
ISBN: 9780137488179

검증된 단계별 안내

Understand the relationship between the voltage and the number of turns in a transformer. This is governed by the transformer equation:

\frac{V_{s}}{V_{p}} = \frac{N_{s}}{N_{p}}, where V_{s} and V_{p} are the secondary and primary voltages, and N_{s} and N_{p} are the number of turns in the secondary and primary coils, respectively.

Substitute the given values into the transformer equation. The primary voltage Vp is 117 V, the secondary voltage Vs is 13,500 V, and the number of turns in the primary coil Np is 172.

Rearrange the equation to solve for the number of turns in the secondary coil Ns. The equation becomes: Ns = VsVp × Np.

Perform the substitution: Ns = 13500117 × 172. This sets up the calculation for the number of turns in the secondary coil.

Simplify the expression to find the value of Ns. This involves dividing 13,500 by 117 and then multiplying the result by 172.

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Transformers

Transformers are electrical devices that transfer electrical energy between two or more circuits through electromagnetic induction. They consist of primary and secondary coils, where the voltage change is proportional to the ratio of the number of turns in each coil. This principle allows transformers to either step up (increase) or step down (decrease) voltage levels.

Turns Ratio

The turns ratio in 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 a critical factor in determining how the voltage changes between the primary and secondary sides. The formula for the turns ratio is given by Vp/Vs = Np/Ns, where V is voltage, N is the number of turns, and the subscripts p and s refer to primary and secondary, respectively.

Voltage Transformation

Voltage transformation in a transformer is governed by the relationship between the primary and secondary voltages and their respective turns. If a transformer steps up voltage, the secondary voltage is greater than the primary voltage, and vice versa for a step-down transformer. This relationship is essential for calculating the number of turns in the secondary coil when the primary voltage and turns are known.

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\vec{B}

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