At the instant when the current in an inductor is increasing at a rate of 0.0640 A/s, the magnitude of the self-induced emf is 0.0160 V. What is the inductance of the inductor?

검증된 단계별 안내

Understand the relationship between the self-induced emf (ε), the inductance (L), and the rate of change of current (di/dt) in an inductor, which is given by the formula:

ε = - L \frac{d}{i} d t

Identify the given values from the problem: the self-induced emf (ε) is 0.0160 V, and the rate of change of current (di/dt) is 0.0640 A/s.

Rearrange the formula to solve for the inductance (L):

L = - \frac{ε}{\frac{d}{i}}

Substitute the given values into the rearranged formula:

L = - \frac{0.0160}{0.0640}

Calculate the value of L using the substituted values to find the inductance of the inductor.

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주요 개념

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

Inductance

Inductance is a property of an electrical conductor that quantifies its ability to induce an electromotive force (emf) when the current flowing through it changes. It is measured in henries (H) and is determined by the physical characteristics of the conductor, such as its shape and the material it is made from.

Self-Induced EMF

Self-induced emf is the voltage generated within an inductor due to a change in current flowing through it. According to Faraday's law of electromagnetic induction, this emf is proportional to the rate of change of current and the inductance of the coil, described by the formula emf = -L * (di/dt), where L is inductance and di/dt is the rate of change of current.

Rate of Change of Current

The rate of change of current refers to how quickly the current flowing through a circuit changes over time, typically measured in amperes per second (A/s). This rate is crucial in determining the self-induced emf in an inductor, as a faster change in current results in a greater emf, according to the relationship emf = -L * (di/dt).