Ch 30: Electromagnetic Induction

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796당신이 사용하는 게 아니라요?교과서 변경

Knight Calc 5th Edition

Ch 30: Electromagnetic Induction

문제 80

30장, 문제 80

In recent years it has been possible to buy a 1.0 F capacitor. This is an enormously large amount of capacitance. Suppose you want to build a 1.0 Hz oscillator with a 1.0 F capacitor. You have a spool of 0.25-mm-diameter wire and a 4.0-cm-diameter plastic cylinder. How long must your inductor be if you wrap it with 2 layers of closely spaced turns?

검증된 단계별 안내

Determine the formula for the frequency of an LC oscillator. The frequency of an LC circuit is given by:

f = \frac{1}{2 π \sqrt{L C}}

, where

f

is the frequency,

L

is the inductance, and

C

is the capacitance.

Rearrange the formula to solve for the inductance

L

L = \frac{1}{4 π^{2} f^{2} C}

. Substitute the given values:

f = 1.0

Hz and

C = 1.0

Calculate the inductance

L

using the formula derived in the previous step. This will give you the required inductance for the oscillator circuit.

Determine the inductance of a solenoid. The inductance of a solenoid is given by:

L = \frac{μ^{0}}{n^{2}}

, where

μ 0

is the permeability of free space (

4π×10-7

T·m/A),

n

is the number of turns per unit length,

A

is the cross-sectional area of the solenoid, and

l

is the length of the solenoid.

Relate the geometry of the solenoid to the inductance. Use the given wire diameter (0.25 mm), cylinder diameter (4.0 cm), and the fact that there are 2 layers of closely spaced turns to calculate the number of turns per unit length

n

and the cross-sectional area

A

. Substitute these values into the solenoid inductance formula and solve for the required length

l

of the inductor.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

10m

도움이 되었나요?

주요 개념

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

Capacitance

Capacitance is the ability of a system to store an electric charge per unit voltage. It is measured in farads (F), where 1 farad is defined as the capacitance of a capacitor that stores one coulomb of charge at one volt. In this question, the 1.0 F capacitor indicates a significant capacity to store charge, which is crucial for the oscillator's operation.

Inductance

Inductance is the property of an electrical conductor that opposes a change in current. It is measured in henries (H) and is essential for the functioning of inductors in circuits. In this scenario, the inductor's design, including its length and the number of turns, will determine its inductance, which, along with the capacitance, will set the frequency of the oscillator.

Oscillator Frequency

The frequency of an oscillator is determined by the values of the inductor and capacitor in the circuit, following the formula f = 1/(2π√(LC)), where f is the frequency, L is the inductance, and C is the capacitance. For a 1.0 Hz oscillator, the relationship between the inductor and capacitor values must be carefully calculated to achieve the desired frequency, making it essential to understand how these components interact.

관련 실천

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교과서 질문

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157

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교과서 질문

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교과서 질문

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교과서 질문

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