Math Problem Statement

Which of the following is a correct statement? (1 point) Lenz's rule states that the direction of the induced current due to change of flux is in such a way as to enforce the cause. A generator is a device that converts electrical energy to mechanical energy. The unit of measurement for the inductance of an inductor is Ampere / second All of the other statements are correct. The self induced emf in an inductor is proportional to the rate of change of the current flowing in the inductor.

Solution

Let's evaluate each statement individually to determine which one is correct.

  1. Lenz's rule states that the direction of the induced current due to change of flux is in such a way as to enforce the cause.

    • This statement is incorrect. Lenz's Law states that the direction of the induced current is such that it opposes the change in magnetic flux that caused it, not enforces it.
  2. A generator is a device that converts electrical energy to mechanical energy.

    • This statement is incorrect. A generator converts mechanical energy into electrical energy, not the other way around.
  3. The unit of measurement for the inductance of an inductor is Ampere / second.

    • This statement is incorrect. The unit of inductance is the Henry (H), not Ampere/second.
  4. All of the other statements are correct.

    • This statement is incorrect since none of the preceding statements are correct.
  5. The self induced emf in an inductor is proportional to the rate of change of the current flowing in the inductor.

    • This statement is correct. According to Faraday's Law of Induction, the self-induced emf (electromotive force) in an inductor is indeed proportional to the rate of change of current through it, which can be mathematically expressed as ε=LdIdt\varepsilon = -L \frac{dI}{dt}, where LL is the inductance and dIdt\frac{dI}{dt} is the rate of change of current.

Therefore, the correct statement is: The self induced emf in an inductor is proportional to the rate of change of the current flowing in the inductor.

Would you like more details or have any questions about this topic?

Here are some related questions to expand your understanding:

  1. What is Faraday's Law of Induction and how does it relate to inductors?
  2. Can you describe an example where Lenz's Law is applied?
  3. How does a transformer work and what principle does it operate on?
  4. What is the difference between self-inductance and mutual inductance?
  5. How can the inductance of an inductor be increased?
  6. What are some practical applications of inductors in electronic circuits?
  7. How does the back emf in a motor relate to Lenz's Law?
  8. What is the significance of the negative sign in the expression ε=LdIdt\varepsilon = -L \frac{dI}{dt}?

Tip: When studying electromagnetism, always pay attention to the direction of induced currents and fields. Using the right-hand rule can help visualize these directions and understand the physical phenomena better.

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Math Problem Analysis

Mathematical Concepts

Electromagnetism
Faraday's Law of Induction
Inductance

Formulas

\( \varepsilon = -L \frac{dI}{dt} \)

Theorems

Lenz's Law

Suitable Grade Level

Advanced High School