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Assertion : In series L-C-R circuit, vol...

Assertion : In series `L-C-R` circuit, voltage will lead the current function for frequency greater than the resonance frequency.
Reason : At resonance frequency, phase difference between current function and voltage function is zero.

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, we need to analyze both the assertion and the reason provided, and determine their validity in the context of a series L-C-R circuit. ### Step-by-Step Solution: 1. **Understanding the Assertion**: - The assertion states that in a series L-C-R circuit, the voltage will lead the current function for frequencies greater than the resonance frequency. - At resonance, the inductive reactance (XL) equals the capacitive reactance (XC), which means that the circuit behaves purely resistively, and the current and voltage are in phase. 2. **Resonance Frequency**: - The resonance frequency (f₀) occurs when XL = XC. This can be expressed mathematically as: \[ XL = 2\pi f L \quad \text{and} \quad XC = \frac{1}{2\pi f C} \] - Setting these equal gives the resonance frequency: \[ 2\pi f_0 L = \frac{1}{2\pi f_0 C} \implies f_0 = \frac{1}{2\pi \sqrt{LC}} \] 3. **Behavior Above Resonance**: - For frequencies greater than the resonance frequency (f > f₀), the inductive reactance (XL) becomes greater than the capacitive reactance (XC): \[ XL > XC \] - In this case, the circuit behaves as an inductive circuit, where the voltage leads the current. 4. **Understanding the Reason**: - The reason states that at the resonance frequency, the phase difference between the current function and the voltage function is zero. - This is indeed true because at resonance, the impedance (Z) is purely resistive (Z = R), leading to a phase angle (φ) of 0 degrees: \[ \cos(\phi) = \frac{Z}{R} = 1 \implies \phi = 0^\circ \] 5. **Conclusion**: - Both the assertion and the reason are true statements. - However, the reason provided does not directly explain why the assertion is true. The assertion is about the behavior of the circuit at frequencies above resonance, while the reason discusses the behavior at resonance itself. ### Final Answer: - Both the assertion and reason are true, but the reason is not the correct explanation for the assertion. Therefore, the correct answer is option B.

To solve the question, we need to analyze both the assertion and the reason provided, and determine their validity in the context of a series L-C-R circuit. ### Step-by-Step Solution: 1. **Understanding the Assertion**: - The assertion states that in a series L-C-R circuit, the voltage will lead the current function for frequencies greater than the resonance frequency. - At resonance, the inductive reactance (XL) equals the capacitive reactance (XC), which means that the circuit behaves purely resistively, and the current and voltage are in phase. ...
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