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Assertion : In an L-R series circuit in ...

Assertion : In an `L-R` series circuit in `AC`, current in the circuit will decrease with increase in frequency.
Reason : Phase difference between current function and voltage function will increase with increase in frequency.

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 question regarding the assertion and reason in an L-R series circuit in AC, we can break it down into steps: ### Step-by-Step Solution: 1. **Understanding the Assertion**: The assertion states that in an L-R series circuit in AC, the current will decrease with an increase in frequency. 2. **Current in an L-R Circuit**: The current \( I \) in an L-R series circuit can be expressed as: \[ I = \frac{V_{\text{rms}}}{Z} \] where \( Z \) is the impedance of the circuit. 3. **Calculating Impedance**: The impedance \( Z \) in an L-R circuit is given by: \[ Z = \sqrt{R^2 + (X_L)^2} \] where \( X_L = 2\pi f L \) is the inductive reactance. 4. **Substituting Inductive Reactance**: Substituting \( X_L \) into the impedance formula, we get: \[ Z = \sqrt{R^2 + (2\pi f L)^2} \] 5. **Current as a Function of Frequency**: Therefore, the current can be rewritten as: \[ I = \frac{V_{\text{rms}}}{\sqrt{R^2 + (2\pi f L)^2}} \] 6. **Analyzing Current with Frequency**: As the frequency \( f \) increases, the term \( (2\pi f L)^2 \) increases, leading to an increase in \( Z \). Since \( I \) is inversely proportional to \( Z \), the current \( I \) will decrease with an increase in frequency. Thus, the assertion is true. 7. **Understanding the Reason**: The reason states that the phase difference between the current function and the voltage function will increase with an increase in frequency. 8. **Calculating Phase Difference**: The phase difference \( \phi \) can be expressed as: \[ \tan \phi = \frac{X_L}{R} = \frac{2\pi f L}{R} \] As frequency \( f \) increases, \( \tan \phi \) also increases, indicating that the phase difference \( \phi \) increases with frequency. Thus, the reason is also true. 9. **Conclusion**: Both the assertion and the reason are true. However, the reason does not correctly explain the assertion. Therefore, the correct answer is that both statements are true, but the reason is not the correct explanation for the assertion. ### Final Answer: - Assertion: True - Reason: True - Conclusion: The reason is not the correct explanation for the assertion.

To solve the question regarding the assertion and reason in an L-R series circuit in AC, we can break it down into steps: ### Step-by-Step Solution: 1. **Understanding the Assertion**: The assertion states that in an L-R series circuit in AC, the current will decrease with an increase in frequency. 2. **Current in an L-R Circuit**: ...
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