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Assertion : Angular frequency of LC osci...

Assertion : Angular frequency of `LC` oscillations is `2 rad//s` and maximum current in the circuit is `1 A`. Then, maximum rate of change of current should be `2 A//s`.
Reason: `((dI)/(dt))_(max)=(I_(max))omega`

A

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

B

If both Assertion and Reason are true but Reason is not the correct explanation of Assertion

C

If Assertion is true, but the Reason is false.

D

If Assertion is false but the Reason is true.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the given problem, we need to analyze the assertion and the reason provided. **Assertion:** The angular frequency of LC oscillations is \(2 \, \text{rad/s}\) and the maximum current in the circuit is \(1 \, \text{A}\). Then, the maximum rate of change of current should be \(2 \, \text{A/s}\). **Reason:** The maximum rate of change of current is given by the formula: \[ \left( \frac{dI}{dt} \right)_{\text{max}} = I_{\text{max}} \cdot \omega \] ### Step-by-Step Solution: 1. **Identify the given values:** - Angular frequency (\(\omega\)) = \(2 \, \text{rad/s}\) - Maximum current (\(I_{\text{max}}\)) = \(1 \, \text{A}\) 2. **Use the formula for the maximum rate of change of current:** According to the reason provided, we can use the formula: \[ \left( \frac{dI}{dt} \right)_{\text{max}} = I_{\text{max}} \cdot \omega \] 3. **Substitute the known values into the formula:** \[ \left( \frac{dI}{dt} \right)_{\text{max}} = 1 \, \text{A} \cdot 2 \, \text{rad/s} \] 4. **Calculate the maximum rate of change of current:** \[ \left( \frac{dI}{dt} \right)_{\text{max}} = 2 \, \text{A/s} \] 5. **Conclusion:** The assertion that the maximum rate of change of current should be \(2 \, \text{A/s}\) is indeed correct based on the given values and the formula provided. ### Final Answer: - The assertion is true, and the reason is a correct explanation of the assertion.

To solve the given problem, we need to analyze the assertion and the reason provided. **Assertion:** The angular frequency of LC oscillations is \(2 \, \text{rad/s}\) and the maximum current in the circuit is \(1 \, \text{A}\). Then, the maximum rate of change of current should be \(2 \, \text{A/s}\). **Reason:** The maximum rate of change of current is given by the formula: \[ \left( \frac{dI}{dt} \right)_{\text{max}} = I_{\text{max}} \cdot \omega ...
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