A resistor, an inductor, and a capacitor are connected in series?

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SUMMARY

In a series circuit comprising a resistor, inductor, and capacitor connected to an AC source operating at resonance frequency, the current is in phase with the driving voltage. The total voltage across the inductor and capacitor at any instant is zero, confirming that the peak voltage across the capacitor and inductor are equal in magnitude but opposite in phase. Additionally, the peak voltage across the resistor is equal to the peak voltage across the inductor. Therefore, statements 1, 5, and 6 are true, while statements 2, 3, and 4 are false.

PREREQUISITES
  • Understanding of AC circuit theory
  • Knowledge of resonance frequency in RLC circuits
  • Familiarity with phasor representation of voltages and currents
  • Basic principles of impedance in electrical circuits
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  • Learn about phasor diagrams for AC circuits
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Homework Statement



A resistor, inductor, capacitor are connected in series to an AC source. The AC source is operating at the resonance freq. Which are true?
1.The current is in phase with the driving voltage.
2.The peak voltage across the capacitor is greater than the peak voltage across the inductor.
3.The peak voltage across the inductor is greater than the peak voltage across the capacitor.
4.The peak voltage across the resistor is equal to peak voltage across the capacitor.
5.The total voltage across the inductor and the capacitor at any instant is equal to zero.
6.The peak voltage across the resistor is equal to the peak voltage across the inductor.

Homework Equations







The Attempt at a Solution



So the current is in phase with the voltage at resonant frequency.
The total voltage across the inductor and capacitor at any instant is zero.

Would that be all? Or am I missing out on some logic...
 
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accioquote said:

Homework Statement



A resistor, inductor, capacitor are connected in series to an AC source. The AC source is operating at the resonance freq. Which are true?
1.The current is in phase with the driving voltage.
2.The peak voltage across the capacitor is greater than the peak voltage across the inductor.
3.The peak voltage across the inductor is greater than the peak voltage across the capacitor.
4.The peak voltage across the resistor is equal to peak voltage across the capacitor.
5.The total voltage across the inductor and the capacitor at any instant is equal to zero.
6.The peak voltage across the resistor is equal to the peak voltage across the inductor.

Homework Equations



The Attempt at a Solution



So the current is in phase with the voltage at resonant frequency.
The total voltage across the inductor and capacitor at any instant is zero.

Would that be all? Or am I missing out on some logic...
That seems right to me .
 

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