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Questions and Answers
What is the value of capacitance at resonance in a series circuit with a 20-ohm resistance, a 150 mH inductance, and a supply voltage of $v = 100 \sin 377t$?
What is the value of capacitance at resonance in a series circuit with a 20-ohm resistance, a 150 mH inductance, and a supply voltage of $v = 100 \sin 377t$?
- 34.65 µF
- 47 uF (correct)
- 42 µF
- 72.57 µF
At what frequency will a circuit with a 5 mH pure inductance connected in parallel with a one microfarad capacitor be antiresonant?
At what frequency will a circuit with a 5 mH pure inductance connected in parallel with a one microfarad capacitor be antiresonant?
- 250 Hz
- 2250 Hz (correct)
- 100 Hz
- 60 Hz
A 5-ohm resistor is in series with a 442.1 µF capacitor, which is in parallel with a 21.22 mH inductor. Solve for the frequency where the inductive reactance equals the capacitive reactance in magnitude.
A 5-ohm resistor is in series with a 442.1 µF capacitor, which is in parallel with a 21.22 mH inductor. Solve for the frequency where the inductive reactance equals the capacitive reactance in magnitude.
- none of these
- 50 Hz
- 51 Hz
- 52 Hz (correct)
A coil has a resistance of 50 ohms and a reactance of 100 ohms. It's shunted by a capacitor with negligible losses. What capacitive reactance is needed for the voltage across the coil to be in phase with the total supplied current?
A coil has a resistance of 50 ohms and a reactance of 100 ohms. It's shunted by a capacitor with negligible losses. What capacitive reactance is needed for the voltage across the coil to be in phase with the total supplied current?
Three impedances Za, Zb, and Zc are connected in parallel. At 60 Hz, Za = j8, Zb = -j2, and Zc = 5 ohms. Find the frequency at resonance.
Three impedances Za, Zb, and Zc are connected in parallel. At 60 Hz, Za = j8, Zb = -j2, and Zc = 5 ohms. Find the frequency at resonance.
A resistor R is in parallel with a 20-ohm inductive reactance. The combination is in series with a 5-ohm capacitive reactance. Find R for a unity power factor of the resultant impedance.
A resistor R is in parallel with a 20-ohm inductive reactance. The combination is in series with a 5-ohm capacitive reactance. Find R for a unity power factor of the resultant impedance.
A coil has a resistance of 50 ohms and a reactance of 70 ohms. A capacitor is connected in parallel to produce resonance. The source voltage is 120 V. What power is drawn by the circuit?
A coil has a resistance of 50 ohms and a reactance of 70 ohms. A capacitor is connected in parallel to produce resonance. The source voltage is 120 V. What power is drawn by the circuit?
A coil is supplied with 200 volts and draws 2 amperes (RMS) at a 0.707 lagging power factor. What is the quality factor (Q) of the coil?
A coil is supplied with 200 volts and draws 2 amperes (RMS) at a 0.707 lagging power factor. What is the quality factor (Q) of the coil?
What is the impedance of a series RLC circuit at resonance?
What is the impedance of a series RLC circuit at resonance?
Which of the following statements is true regarding a parallel resonant circuit?
Which of the following statements is true regarding a parallel resonant circuit?
Flashcards
Capacitance at Resonance
Capacitance at Resonance
The value of capacitance that results in resonance for the given series circuit is 47 µF.
Antiresonance Frequency
Antiresonance Frequency
The frequency at which the parallel circuit exhibits antiresonance is 2250 Hz.
Equal Reactance Frequency
Equal Reactance Frequency
The frequency at which the inductive reactance equals the capacitive reactance in magnitude is 52 Hz.
Capacitive Reactance for In-Phase Condition
Capacitive Reactance for In-Phase Condition
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Resonance Frequency of Parallel Impedances
Resonance Frequency of Parallel Impedances
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Resistance for Unity Power Factor
Resistance for Unity Power Factor
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Power at Resonance
Power at Resonance
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Coil Quality Factor
Coil Quality Factor
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Study Notes
- Problems on AC circuits are presented, covering series and parallel RLC circuits, resonance, and power factor correction
Series RLC Circuit Resonance
- A series circuit has a 20-ohm resistance, a 150 mH inductance, and an unknown capacitance, and is supplied with a voltage v = 100 sin 377t
- Resonance occurs when the capacitive reactance equals the inductive reactance
- The capacitance value at resonance is 47 µF
Parallel LC Circuit Anti-resonance
- Anti-resonance in a parallel LC circuit happens when the inductive and capacitive reactances are equal, leading to maximum impedance
- A 5 mH pure inductance is connected in parallel with a one microfarad capacitor will be anti-resonant at 2250 Hz
Series-Parallel RLC Circuit
- A 5-ohm resistor in series with a 442.1 µF capacitor, in parallel with a 21.22 mH inductor.
- The frequency at which inductive reactance equals capacitive reactance is 52 Hz
Parallel RLC Circuit - In Phase Condition
- A coil has a resistance of 50 ohms and a reactance of 100 ohms, shunted by a capacitor with negligible losses
- For the voltage across the coil to be in phase with the total current, the capacitor's reactance must be 125 ohms
- This condition is achieved when the parallel combination resonates, resulting in a unity power factor
Parallel Impedances at Resonance
- Three impedances Za, Zb, and Zc are connected in parallel
- At 60 Hz, Za = j8, Zb = -j2, and Zc = 5 ohms
- The frequency at resonance is 30 Hz
Power Factor Correction
- A resistor R in parallel with a 20-ohm inductive reactance, connected in series with a 5-ohm capacitive reactance
- For the resultant impedance to have a unity power factor, the value of R must be 11.55 ohms.
- Unity power factor means that the circuit is purely resistive
Parallel Resonance and Power Consumption
- A coil with 50 ohms resistance and 70 ohms reactance is connected in parallel with a capacitor to achieve resonance.
- With a 120 V source voltage, the circuit draws 97 W of power
Coil Quality Factor
- A coil supplied with 200 volts draws 2 amperes (RMS) at a 0.707 lagging power factor
- The quality factor (Q) of the coil is 1
- Q is the ratio of reactance to resistance in the coil
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