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In series LCR circuit voltage leads the ...

In series LCR circuit voltage leads the current. When
(Given that `omega_(0)` = resonant angular frequency)

A

`omega lt omega_(0)`

B

`omega = omega_(0)`

C

`omega gt omega_(0)`

D

None of these

Text Solution

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The correct Answer is:
To determine the condition under which the voltage leads the current in a series LCR circuit, we need to analyze the relationship between the angular frequency (ω) and the resonant angular frequency (ω₀). ### Step-by-Step Solution: 1. **Understand the Circuit**: In a series LCR circuit, we have an inductor (L), a capacitor (C), and a resistor (R) connected in series. The behavior of the circuit is influenced by the frequency of the applied voltage. 2. **Resonant Frequency**: The resonant angular frequency (ω₀) is given by the formula: \[ \omega_0 = \frac{1}{\sqrt{LC}} \] At this frequency, the inductive reactance (X_L = ωL) and capacitive reactance (X_C = \frac{1}{ωC}) are equal, leading to a purely resistive circuit. 3. **Phase Relationship**: In an LCR circuit: - If the applied frequency (ω) is less than the resonant frequency (ω₀), the circuit is capacitive, and the current leads the voltage. - If the applied frequency (ω) is greater than the resonant frequency (ω₀), the circuit is inductive, and the voltage leads the current. 4. **Condition for Voltage Leading Current**: Therefore, for the voltage to lead the current, the condition must be: \[ \omega > \omega_0 \] 5. **Conclusion**: Hence, the final answer is that in a series LCR circuit, the voltage leads the current when the applied frequency (ω) is greater than the resonant frequency (ω₀). ### Final Answer: Voltage leads the current in a series LCR circuit when: \[ \omega > \omega_0 \]
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