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A: At any instant, if the current throug...

A: At any instant, if the current through an inductor is zero, then the induced emf will also be zero.
R: In one time constant, the current flows to 37 percent of its maximum value in a series LR circuit.

A

If both Assertion & Reason are true and the reason is the correct explanation of the assertion.

B

If both Assertion & Reason are true but the reason is not the correct explanation of the assertion.

C

If Assertion is true statement but Reason is false.

D

If both Assertion and Reason are false statements.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the given problem, we need to analyze both the assertion (A) and the reason (R) provided in the question. ### Step-by-Step Solution: 1. **Understanding the Assertion (A)**: - The assertion states that if the current through an inductor is zero at any instant, then the induced emf will also be zero. - According to Faraday's Law of Electromagnetic Induction, an emf is induced in a circuit when there is a change in magnetic flux through the circuit. - If the current is zero, it does not necessarily mean that the induced emf is zero. An emf can be induced due to a changing magnetic field even if the current is not flowing. Therefore, the assertion is **false**. 2. **Understanding the Reason (R)**: - The reason states that in one time constant, the current flows to 37 percent of its maximum value in a series LR circuit. - The time constant (τ) in an LR circuit is defined as τ = L/R, where L is the inductance and R is the resistance. - The current in an LR circuit as a function of time is given by the equation: \[ I(t) = I_0(1 - e^{-t/\tau}) \] where \(I_0\) is the maximum current. - At \(t = \tau\), substituting into the equation gives: \[ I(\tau) = I_0(1 - e^{-1}) \approx 0.632I_0 \] This means that at one time constant, the current reaches approximately 63.2% of its maximum value, not 37%. Therefore, the reason is also **false**. 3. **Conclusion**: - Both the assertion (A) and the reason (R) are false. Thus, the correct answer is that both statements are incorrect. ### Final Answer: Both the assertion and the reason are false. ---
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