Find the phase differencw between voltage and current in series LCR circuit at half power frequencies.?

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Answer

At half power frequency current is 1÷root 2 of max. current so I=Imsinwt and I÷root2=Isin theta, I gets cancelled and sin theta=1÷root 2 and theta=45 degree

Answer

Answer

Phase Difference between Voltage and Current in Series LCR Circuit at Half Power Frequencies

To understand the phase difference between voltage and current in a series LCR circuit at half power frequencies, let's first analyze the behavior of each component in the circuit.

L (Inductor):
- An inductor is a passive electronic component that stores energy in its magnetic field.
- In an AC circuit, the inductor opposes any changes in current by inducing a voltage that is proportional to the rate of change of current.
- The voltage across an inductor leads the current by 90 degrees in an ideal scenario.

C (Capacitor):
- A capacitor is another passive electronic component that stores energy in its electric field.
- In an AC circuit, the capacitor opposes any changes in voltage by storing and releasing charge.
- The voltage across a capacitor lags the current by 90 degrees in an ideal scenario.

R (Resistor):
- A resistor is a passive electronic component that dissipates energy as heat.
- In an AC circuit, the resistor does not introduce any phase shift between voltage and current as it has no reactive properties.

Series LCR Circuit:
- A series LCR circuit consists of a resistor, inductor, and capacitor connected in series.
- The impedance (Z) of the circuit is given by the vector sum of the resistive (R), inductive (XL), and capacitive (XC) components: Z = R + j(XL - XC).
- At resonance (when XL = XC), the impedance is purely resistive, and the phase difference between voltage and current is zero.
- However, at frequencies other than resonance, the impedance is a complex number with both real and imaginary parts, resulting in a phase difference between voltage and current.

Half Power Frequencies:
- Half power frequencies are the frequencies at which the power dissipated in the circuit is half of the maximum power.
- At these frequencies, the impedance of the circuit is equal to the resistance, i.e., Z = R.
- To find the half power frequencies, we can equate the magnitude of the reactance to the resistance: |XL| = |XC|.
- At these frequencies, the phase difference between voltage and current is 45 degrees.

Summary:
- In a series LCR circuit, the phase difference between voltage and current at half power frequencies is 45 degrees.
- At resonance, the phase difference is zero, and at frequencies other than resonance, the phase difference depends on the impedance of the circuit.
- The inductor and capacitor introduce 90-degree phase shifts individually, but at half power frequencies, their combined effect results in a 45-degree phase difference.
- Understanding the phase difference is essential in analyzing the behavior and performance of series LCR circuits in various applications.

Similar NEET Doubts

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What is the phase difference between voltage and current in a LCR series circuit of resonance?

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