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In a 1-phase series RL circuit fed by a voltage source, the resistance and reactance values are 4 ohms each.
- a)the current leads the voltage by 450
- b)the current lags the voltage by 450
- c)the current lags the voltage by 600
- d)None of the above
Correct answer is option 'B'. Can you explain this answer?
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In a 1-phase series RL circuit fed by a voltage source, the resistanc...
In a 1-phase series RL circuit is fed by a voltage source. The resistance and reactance values are 4 ohm
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Z = 4j4
tanθ = 1
θ = 450
Current lags the voltage by 450
Most Upvoted Answer
In a 1-phase series RL circuit fed by a voltage source, the resistanc...
Explanation:
To determine whether the current leads or lags the voltage in a 1-phase series RL circuit, we need to compare the phase angles of the current and voltage.
Phase Angle:
The phase angle is the relative position of the current or voltage waveform in relation to a reference waveform. It is measured in degrees or radians.
Impedance:
The impedance of a series RL circuit can be calculated using the formula: Z = √(R^2 + X^2), where R is the resistance and X is the reactance.
Phase Angle Relationship:
The phase angle relationship between the current and voltage in a series RL circuit can be determined using the arctan formula:
θ = arctan(X/R), where θ is the phase angle.
Given:
Resistance (R) = 4 ohms
Reactance (X) = 4 ohms
Calculations:
1. Calculate the impedance of the circuit:
Z = √(R^2 + X^2)
Z = √(4^2 + 4^2)
Z = √(16 + 16)
Z = √32
Z ≈ 5.66 ohms
2. Calculate the phase angle:
θ = arctan(X/R)
θ = arctan(4/4)
θ = arctan(1)
θ ≈ 45 degrees
Analysis:
The phase angle calculated is approximately 45 degrees. Since the reactance and resistance values are equal, the current and voltage waveforms are in phase. Therefore, the current lags the voltage by 45 degrees.
Answer:
The current lags the voltage by 45 degrees. Therefore, the correct answer is option 'B' - the current lags the voltage by 450.
To determine whether the current leads or lags the voltage in a 1-phase series RL circuit, we need to compare the phase angles of the current and voltage.
Phase Angle:
The phase angle is the relative position of the current or voltage waveform in relation to a reference waveform. It is measured in degrees or radians.
Impedance:
The impedance of a series RL circuit can be calculated using the formula: Z = √(R^2 + X^2), where R is the resistance and X is the reactance.
Phase Angle Relationship:
The phase angle relationship between the current and voltage in a series RL circuit can be determined using the arctan formula:
θ = arctan(X/R), where θ is the phase angle.
Given:
Resistance (R) = 4 ohms
Reactance (X) = 4 ohms
Calculations:
1. Calculate the impedance of the circuit:
Z = √(R^2 + X^2)
Z = √(4^2 + 4^2)
Z = √(16 + 16)
Z = √32
Z ≈ 5.66 ohms
2. Calculate the phase angle:
θ = arctan(X/R)
θ = arctan(4/4)
θ = arctan(1)
θ ≈ 45 degrees
Analysis:
The phase angle calculated is approximately 45 degrees. Since the reactance and resistance values are equal, the current and voltage waveforms are in phase. Therefore, the current lags the voltage by 45 degrees.
Answer:
The current lags the voltage by 45 degrees. Therefore, the correct answer is option 'B' - the current lags the voltage by 450.
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