UNIT-3 Single Phase AC Circuit
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Questions and Answers

What is the relationship between the maximum current and voltage in a purely resistive circuit?

  • The current leads the voltage by 90 degrees.
  • The maximum current is equal to the maximum voltage.
  • The current and voltage are in phase. (correct)
  • The current lags behind the voltage by 90 degrees.

    • In a purely inductive circuit, how does the current relate to the voltage?

  • The current is in phase with the voltage.
  • The current has no relation to the voltage.
  • The current lags behind the voltage by 90 degrees. (correct)
  • The current leads the voltage by 90 degrees.

    • What defines the RMS value of an AC wave?

  • The difference between peak voltage and average voltage.
  • The average of the maximum values of current and voltage.
  • The peak current divided by the peak voltage.
  • The square root of the average of the squares of instantaneous values. (correct)

    • What happens to the current in a circuit containing only a capacitor?

    <p>The current leads the voltage by 90 degrees.</p> Signup and view all the answers

    In an RL series circuit, what does the impedance represent?

    <p>The total opposition to the flow of alternating current.</p> Signup and view all the answers

    What is the equation for average voltage in terms of peak voltage for sinusoidal waves?

    <p>Vavg = 0.636 Vmax</p> Signup and view all the answers

    Which of the following functions describes the instantaneous voltage in a purely resistive circuit?

    <p>v = Vm sin(wt)</p> Signup and view all the answers

    In an AC circuit consisting solely of an inductor, what is the relationship between voltage and current?

    <p>The current lags the voltage by 90 degrees.</p> Signup and view all the answers

    What describes a purely resistive AC circuit's behavior with respect to power?

    <p>Power is dissipated and current is maximized.</p> Signup and view all the answers

    What is the phase difference observed in a pure capacitive AC circuit?

    <p>Current leads voltage by 90 degrees.</p> Signup and view all the answers

    What does the term 'amplitude' refer to in an AC circuit?

    <p>The highest positive or negative value of an alternating quantity</p> Signup and view all the answers

    In terms of AC circuits, what is defined as the time taken to complete one cycle?

    <p>Time period</p> Signup and view all the answers

    What does the peak-to-peak value represent in an AC waveform?

    <p>The difference between the maximum positive and maximum negative values</p> Signup and view all the answers

    How is frequency defined in the context of AC circuits?

    <p>The number of cycles completed in one second</p> Signup and view all the answers

    What denotes the instantaneous value in an AC circuit?

    <p>The value of voltage or current at a specific moment</p> Signup and view all the answers

    What is the relationship between the peak value and the peak-to-peak value in an AC signal?

    <p>The peak value is half of the peak-to-peak value</p> Signup and view all the answers

    In what scenario might the instantaneous value of an AC signal be zero?

    <p>When the polarity of the voltage is changing</p> Signup and view all the answers

    What is the average value of an AC signal usually based on?

    <p>The instantaneous values averaged over the entire cycle</p> Signup and view all the answers

    What defines the waveform in an AC circuit?

    <p>The pattern created by plotting instantaneous values against time</p> Signup and view all the answers

    What does the term 'impedance' (Z) represent in an RC series circuit?

    <p>The total opposition to current flow</p> Signup and view all the answers

    In an RLC series circuit, when the inductive reactance (XL) is greater than the capacitive reactance (XC), what does this indicate about the circuit's behavior?

    <p>The phase angle is positive and current lags behind voltage.</p> Signup and view all the answers

    Which formula is used to calculate the reactance of a capacitor in an RLC circuit?

    <p>XC = 1 / (2πfC)</p> Signup and view all the answers

    How is the current (I) calculated in a series RLC circuit?

    <p>I = V / Z</p> Signup and view all the answers

    What is the relationship between voltage across the resistance (VR) and current (I) in an RLC series circuit?

    <p>VR is in phase with current I</p> Signup and view all the answers

    If the total impedance (Z) of a circuit is determined to be approximately 354.89 Ohms, what would be the expected current (I) when connected to a 250V supply?

    <p>0.705 A</p> Signup and view all the answers

    Which of the following statements is true about the power factor (PF) when measuring an RLC circuit with R = 200 Ohms and Z = 354.89 Ohms?

    <p>PF is equal to 0.563</p> Signup and view all the answers

    What can be inferred if in an RLC series circuit the voltages across the capacitor (VC) and inductor (VL) are 224.41 V and 17.72 V respectively?

    <p>The voltage across the inductor exceeds the voltage across the capacitor.</p> Signup and view all the answers

    What is the total voltage (V) across the components when a RLC series circuit has a voltage across the resistor (VR) of 141 V and a voltage across the capacitor (VC) of 224.41 V?

    <p>V = √(VR² + VC²)</p> Signup and view all the answers

    What is the highest positive or negative value obtained by an alternating quantity during one full cycle called?

    <p>Amplitude</p> Signup and view all the answers

    What is the time taken by a voltage or current to complete one cycle known as?

    <p>Time period</p> Signup and view all the answers

    How is frequency expressed?

    <p>In hertz (Hz)</p> Signup and view all the answers

    What does the peak-to-peak value of a sine wave represent?

    <p>Twice the maximum peak value</p> Signup and view all the answers

    What is defined as the shape created by charting the instantaneous values of an alternating variable?

    <p>Waveform</p> Signup and view all the answers

    During a complete cycle of an AC signal, how many maximum or peak values are there?

    <p>Two maximum values</p> Signup and view all the answers

    Which of the following best describes an instantaneous value in an AC signal?

    <p>The value at a specific point in time</p> Signup and view all the answers

    What is the value called when you take the average of the instantaneous values of alternating current over a complete cycle?

    <p>Average value</p> Signup and view all the answers

    What does the term 'instantaneous value' indicate in an AC circuit?

    <p>The value at a particular instant in time</p> Signup and view all the answers

    In a sine wave, how does the peak value relate to the peak-to-peak value?

    <p>The peak value is one-half of the peak-to-peak value</p> Signup and view all the answers

    What is the formula for total impedance (Z) in an RLC series circuit?

    <p>Z = v((XL - XC)^2 + R^2)</p> Signup and view all the answers

    How does the voltage across the capacitor (VC) behave in relation to the current (I) in an RLC circuit?

    <p>VC lags I by 90 degrees</p> Signup and view all the answers

    In a purely resistive AC circuit, what is the phase relationship between voltage and current?

    <p>Current and voltage are in phase</p> Signup and view all the answers

    When XL < XC in an RLC series circuit, what is the resulting phase angle?

    <p>The phase angle is negative</p> Signup and view all the answers

    What represents the total opposition to current flow in an RLC series circuit?

    <p>Impedance (Z)</p> Signup and view all the answers

    What happens to the current in a purely inductive circuit in relation to the voltage?

    <p>Current lags voltage by 90 degrees</p> Signup and view all the answers

    How is the average voltage (Vavg) of a sinusoidal wave expressed in terms of maximum voltage (Vmax)?

    <p>Vavg = 0.636 Vmax</p> Signup and view all the answers

    What is the power factor (PF) when R = 200 Ohms and Z = 354.89 Ohms?

    <p>0.563</p> Signup and view all the answers

    What does the RMS value of an AC wave allow us to determine?

    <p>The amount of DC power that generates the same heating effect</p> Signup and view all the answers

    What is the voltage across the resistor (VR) when the current (I) is approximately 0.705 A and R is 200 Ohms?

    <p>141 V</p> Signup and view all the answers

    In an AC RLC series circuit, how does the voltage across the inductor (VL) relate to the current (I)?

    <p>VL leads I by 90 degrees</p> Signup and view all the answers

    In a circuit with only a capacitor, how does the current relate to the voltage?

    <p>Current leads voltage by 90 degrees</p> Signup and view all the answers

    What is the effective value of current in terms of maximum current (Im) for a purely inductive circuit?

    <p>I = Im sin(wt - 90 degrees)</p> Signup and view all the answers

    If the total voltage (V) across an RLC series circuit is given as 250 V, what can be inferred if the voltage across the capacitor (VC) is 224.41 V?

    <p>VR must be lower than VC</p> Signup and view all the answers

    Which of the following formulas represents the impedance (Z) in an RL series circuit?

    <p>Z = √(R^2 + XL^2)</p> Signup and view all the answers

    What is the inductive reactance (XL) formula in an RLC circuit?

    <p>XL = 2 * p * f * L</p> Signup and view all the answers

    What is the value of the reactance of the inductor (X_L) if L = 0.08 H and frequency (f) = 50 Hz?

    <p>25.13 Ohms</p> Signup and view all the answers

    In an RC series circuit, which of the following components significantly affects the current flow?

    <p>Both the resistor (R) and the capacitor (C)</p> Signup and view all the answers

    What does the term inductive reactance (XL) refer to in a purely inductive circuit?

    <p>The resistance offered by the inductor to the flow of Alternating Current</p> Signup and view all the answers

    In an RL series circuit, what is represented by the term 'Z'?

    <p>The total opposition to current flow</p> Signup and view all the answers

    What is the peak-to-peak value of a sine wave if its peak value is 12V?

    <p>24V</p> Signup and view all the answers

    How is the frequency of an AC signal expressed mathematically?

    <p>f = 1/T</p> Signup and view all the answers

    If the instantaneous voltage at a specific point in time is equal to its peak value, what can be inferred about the time within the cycle?

    <p>It is at the maximum point of increase.</p> Signup and view all the answers

    Which of the following best represents the average value of an alternating current over a complete cycle?

    <p>The sum of instantaneous values divided by one complete cycle.</p> Signup and view all the answers

    What term describes the shape created by plotting instantaneous values against time in an AC circuit?

    <p>Waveform</p> Signup and view all the answers

    If the time period of an AC signal is 0.02 seconds, what is its frequency?

    <p>20 Hz</p> Signup and view all the answers

    How many instantaneous values can exist between the peak value of an AC signal and zero?

    <p>Infinitely many</p> Signup and view all the answers

    What is the time taken to complete one full cycle of voltage or current known as?

    <p>Time Period</p> Signup and view all the answers

    In an AC signal, the instantaneous value can be equal to its peak value at which point in the cycle?

    <p>At the maximum of the positive half-cycle</p> Signup and view all the answers

    What denotes the maximum voltage and current values in an AC signal?

    <p>Em and Im</p> Signup and view all the answers

    What happens to the current in a purely inductive AC circuit in relation to the voltage?

    <p>The current lags the voltage by 90 degrees.</p> Signup and view all the answers

    What does the term inductive reactance refer to in a purely inductive circuit?

    <p>Opposition to alternating current flow due to inductance.</p> Signup and view all the answers

    In an AC circuit with only a capacitor, how is the current expressed in relation to the voltage?

    <p>The current leads the voltage by 90 degrees.</p> Signup and view all the answers

    What is the relationship between RMS values and average values in AC circuits?

    <p>RMS values provide the same heating effect as equivalent DC power.</p> Signup and view all the answers

    In the context of an RL series circuit, what does the term 'impedance' represent?

    <p>The total opposition to current flow offered by the resistance and inductance.</p> Signup and view all the answers

    What occurs in a purely resistive AC circuit when voltage reaches its maximum?

    <p>The power factor equals one.</p> Signup and view all the answers

    How is the instantaneous value of current defined in a purely resistive circuit at its peak voltage?

    <p>It equals the peak voltage divided by resistance.</p> Signup and view all the answers

    What is true about the phase relationship in an RL series circuit?

    <p>Voltage lags current due to inductive reactance.</p> Signup and view all the answers

    What factor does the average voltage depend on in a sinusoidal wave?

    <p>The maximum or peak voltage only.</p> Signup and view all the answers

    What represents the time it takes for one complete cycle of an alternating current?

    <p>Period.</p> Signup and view all the answers

    What is the relationship between total voltage (V) and the reactance in an RLC circuit?

    <p>V = I * Z</p> Signup and view all the answers

    What indicates a purely resistive circuit when analyzing the phase angle in an RLC circuit?

    <p>XL = XC</p> Signup and view all the answers

    Given a circuit with R = 200 Ohms, L = 0.08 H, and C = 100 µF, what is the approximate value of the inductive reactance (XL) at 50 Hz?

    <p>25.13 Ohms</p> Signup and view all the answers

    In an RLC series circuit, what leads the current by an angle of 90 degrees?

    <p>Voltage across inductor (VL)</p> Signup and view all the answers

    Which of the following expresses the total opposition (impedance) in an RLC circuit correctly?

    <p>Z = sqrt(R^2 + (XL - XC)^2)</p> Signup and view all the answers

    When XL < XC in an RLC circuit, what is the general behavior of current in relation to voltage?

    <p>Current leads voltage</p> Signup and view all the answers

    What is the power factor (PF) when R = 200 Ohms and Z = 354.89 Ohms?

    <p>0.563</p> Signup and view all the answers

    If the voltage across the capacitor (VC) is calculated to be approximately 224.41 V, what does this suggest about the current in the circuit?

    <p>Current is leading the voltage</p> Signup and view all the answers

    What is the result when calculating the power consumed in the circuit if V = 250 V, I = 0.705 A, and PF = 0.563?

    <p>98.95 W</p> Signup and view all the answers

    What condition exists when the voltages across the inductor (VL) and capacitor (VC) are equal in an RLC circuit?

    <p>XL = XC</p> Signup and view all the answers

    Study Notes

    Single Phase AC Circuit

    • Amplitude: Peak value of an alternating quantity in one full cycle; represented by Em or Vm for voltage, Im for current.
    • One Full Cycle: Consists of positive and negative values completing 360 degrees electrically.
    • Instantaneous Value: Voltage or current at any specific moment, denoted by "i" for current or "e" for voltage.
    • Frequency (f): Number of cycles per second, measured in Hertz (Hz); f = 1/T, where T is the time period.
    • Time Period (T): Time taken to complete one cycle in seconds.
    • Waveform: Graphical representation of instantaneous values against time or angle, showing alternating voltage/current trends.
    • Peak vs. Peak-to-Peak Value: Peak value measures from zero to max value; peak-to-peak value is twice the peak value, encompassing both positive and negative peaks.

    Average Value of AC

    • Defined as the average of instantaneous values over one complete cycle; for sinusoidal waveforms, Vavg = 0.636 Vmax and Iavg = 0.636 Imax.
    • Average value for full cycles of asymmetrical waves (sinusoidal) equals zero because positive and negative half-cycles cancel out.

    RMS Value of AC Wave

    • RMS (Root Mean Square) value calculates the equivalent DC power that produces the same heating effect; crucial in powering aspects.

    Purely Resistive Circuit

    • Contains only resistance (R ohms), with no inductance or capacitance effects.
    • Voltage and current are in phase; they reach maximum values simultaneously.
    • Current can be calculated as i = Vm/R sin(ωt), indicating that Imsin(ωt) describes current.

    Purely Inductive Circuit

    • Contains only inductance; current lags voltage by 90 degrees.
    • Voltage is given by v = Vm sin(ωt).
    • Inductive reactance (XL) opposes current changes; maximum current occurs at i = Im sin(ωt - π/2), demonstrating the phase lag.

    AC Circuit with Capacitor Only

    • Only capacitance present; current leads voltage by 90 degrees.
    • Voltage is v = Vm sin(ωt) and current i = CmVm cos(ωt).
    • Maximum current occurs at i = Im sin(ωt + π/2), representing the phase lead.

    RL Series Circuit

    • Series combination of pure resistance (R) and pure inductance (L); current (I) flows equally through both elements.
    • Voltage relationships: VR = IR and VL = IXL.
    • Total voltage (V) calculated from V = √(VR² + VL²) where Z = √(R² + XL²) represents impedance.

    RC Series Circuit

    • Comprises pure resistance (R) and pure capacitance (C).
    • Voltage across components: VR = IR and VC = IXC.
    • Total impedance is Z = √(R² + XC²).

    RLC Series Circuit

    • Combines resistance (R), inductance (L), and capacitance (C) in series.
    • Current through all components is the same; inductor voltage leads by 90°, while capacitor voltage lags by 90°.
    • Impedance calculated as Z = √(R² + (XL - XC)²); phase relationships determine the circuit behavior:
      • XL > XC: circuit acts inductively (current lags voltage).
      • XL < XC: circuit acts capacitively (current leads voltage).
      • XL = XC: circuit behaves resistively (current in phase with voltage).

    Example Problem

    • Given an RLC circuit with R = 200Ω, L = 0.08H, C = 100μF, and a supply of 250V at 50Hz:
      • Reactance Calculations:
        • XR = R = 200Ω.
        • XL ≈ 25.13Ω.
        • XC ≈ 318.31Ω.
      • Impedance (Z): Z ≈ 354.89Ω.
      • Current (I): I ≈ 0.705A.
      • Power Factor (PF): PF ≈ 0.563.
      • Power Consumed (P): P ≈ 98.95W.
      • Voltage across Components:
        • Voltage across Resistor (VR) ≈ 141V.
        • Voltage across Inductor (VL) ≈ 17.72V.
        • Voltage across Capacitor (VC) ≈ 224.41V.

    Single Phase AC Circuit

    • Amplitude: Peak value of an alternating quantity in one full cycle; represented by Em or Vm for voltage, Im for current.
    • One Full Cycle: Consists of positive and negative values completing 360 degrees electrically.
    • Instantaneous Value: Voltage or current at any specific moment, denoted by "i" for current or "e" for voltage.
    • Frequency (f): Number of cycles per second, measured in Hertz (Hz); f = 1/T, where T is the time period.
    • Time Period (T): Time taken to complete one cycle in seconds.
    • Waveform: Graphical representation of instantaneous values against time or angle, showing alternating voltage/current trends.
    • Peak vs. Peak-to-Peak Value: Peak value measures from zero to max value; peak-to-peak value is twice the peak value, encompassing both positive and negative peaks.

    Average Value of AC

    • Defined as the average of instantaneous values over one complete cycle; for sinusoidal waveforms, Vavg = 0.636 Vmax and Iavg = 0.636 Imax.
    • Average value for full cycles of asymmetrical waves (sinusoidal) equals zero because positive and negative half-cycles cancel out.

    RMS Value of AC Wave

    • RMS (Root Mean Square) value calculates the equivalent DC power that produces the same heating effect; crucial in powering aspects.

    Purely Resistive Circuit

    • Contains only resistance (R ohms), with no inductance or capacitance effects.
    • Voltage and current are in phase; they reach maximum values simultaneously.
    • Current can be calculated as i = Vm/R sin(ωt), indicating that Imsin(ωt) describes current.

    Purely Inductive Circuit

    • Contains only inductance; current lags voltage by 90 degrees.
    • Voltage is given by v = Vm sin(ωt).
    • Inductive reactance (XL) opposes current changes; maximum current occurs at i = Im sin(ωt - π/2), demonstrating the phase lag.

    AC Circuit with Capacitor Only

    • Only capacitance present; current leads voltage by 90 degrees.
    • Voltage is v = Vm sin(ωt) and current i = CmVm cos(ωt).
    • Maximum current occurs at i = Im sin(ωt + π/2), representing the phase lead.

    RL Series Circuit

    • Series combination of pure resistance (R) and pure inductance (L); current (I) flows equally through both elements.
    • Voltage relationships: VR = IR and VL = IXL.
    • Total voltage (V) calculated from V = √(VR² + VL²) where Z = √(R² + XL²) represents impedance.

    RC Series Circuit

    • Comprises pure resistance (R) and pure capacitance (C).
    • Voltage across components: VR = IR and VC = IXC.
    • Total impedance is Z = √(R² + XC²).

    RLC Series Circuit

    • Combines resistance (R), inductance (L), and capacitance (C) in series.
    • Current through all components is the same; inductor voltage leads by 90°, while capacitor voltage lags by 90°.
    • Impedance calculated as Z = √(R² + (XL - XC)²); phase relationships determine the circuit behavior:
      • XL > XC: circuit acts inductively (current lags voltage).
      • XL < XC: circuit acts capacitively (current leads voltage).
      • XL = XC: circuit behaves resistively (current in phase with voltage).

    Example Problem

    • Given an RLC circuit with R = 200Ω, L = 0.08H, C = 100μF, and a supply of 250V at 50Hz:
      • Reactance Calculations:
        • XR = R = 200Ω.
        • XL ≈ 25.13Ω.
        • XC ≈ 318.31Ω.
      • Impedance (Z): Z ≈ 354.89Ω.
      • Current (I): I ≈ 0.705A.
      • Power Factor (PF): PF ≈ 0.563.
      • Power Consumed (P): P ≈ 98.95W.
      • Voltage across Components:
        • Voltage across Resistor (VR) ≈ 141V.
        • Voltage across Inductor (VL) ≈ 17.72V.
        • Voltage across Capacitor (VC) ≈ 224.41V.

    Single Phase AC Circuit

    • Amplitude: Peak value of an alternating quantity in one full cycle; represented by Em or Vm for voltage, Im for current.
    • One Full Cycle: Consists of positive and negative values completing 360 degrees electrically.
    • Instantaneous Value: Voltage or current at any specific moment, denoted by "i" for current or "e" for voltage.
    • Frequency (f): Number of cycles per second, measured in Hertz (Hz); f = 1/T, where T is the time period.
    • Time Period (T): Time taken to complete one cycle in seconds.
    • Waveform: Graphical representation of instantaneous values against time or angle, showing alternating voltage/current trends.
    • Peak vs. Peak-to-Peak Value: Peak value measures from zero to max value; peak-to-peak value is twice the peak value, encompassing both positive and negative peaks.

    Average Value of AC

    • Defined as the average of instantaneous values over one complete cycle; for sinusoidal waveforms, Vavg = 0.636 Vmax and Iavg = 0.636 Imax.
    • Average value for full cycles of asymmetrical waves (sinusoidal) equals zero because positive and negative half-cycles cancel out.

    RMS Value of AC Wave

    • RMS (Root Mean Square) value calculates the equivalent DC power that produces the same heating effect; crucial in powering aspects.

    Purely Resistive Circuit

    • Contains only resistance (R ohms), with no inductance or capacitance effects.
    • Voltage and current are in phase; they reach maximum values simultaneously.
    • Current can be calculated as i = Vm/R sin(ωt), indicating that Imsin(ωt) describes current.

    Purely Inductive Circuit

    • Contains only inductance; current lags voltage by 90 degrees.
    • Voltage is given by v = Vm sin(ωt).
    • Inductive reactance (XL) opposes current changes; maximum current occurs at i = Im sin(ωt - π/2), demonstrating the phase lag.

    AC Circuit with Capacitor Only

    • Only capacitance present; current leads voltage by 90 degrees.
    • Voltage is v = Vm sin(ωt) and current i = CmVm cos(ωt).
    • Maximum current occurs at i = Im sin(ωt + π/2), representing the phase lead.

    RL Series Circuit

    • Series combination of pure resistance (R) and pure inductance (L); current (I) flows equally through both elements.
    • Voltage relationships: VR = IR and VL = IXL.
    • Total voltage (V) calculated from V = √(VR² + VL²) where Z = √(R² + XL²) represents impedance.

    RC Series Circuit

    • Comprises pure resistance (R) and pure capacitance (C).
    • Voltage across components: VR = IR and VC = IXC.
    • Total impedance is Z = √(R² + XC²).

    RLC Series Circuit

    • Combines resistance (R), inductance (L), and capacitance (C) in series.
    • Current through all components is the same; inductor voltage leads by 90°, while capacitor voltage lags by 90°.
    • Impedance calculated as Z = √(R² + (XL - XC)²); phase relationships determine the circuit behavior:
      • XL > XC: circuit acts inductively (current lags voltage).
      • XL < XC: circuit acts capacitively (current leads voltage).
      • XL = XC: circuit behaves resistively (current in phase with voltage).

    Example Problem

    • Given an RLC circuit with R = 200Ω, L = 0.08H, C = 100μF, and a supply of 250V at 50Hz:
      • Reactance Calculations:
        • XR = R = 200Ω.
        • XL ≈ 25.13Ω.
        • XC ≈ 318.31Ω.
      • Impedance (Z): Z ≈ 354.89Ω.
      • Current (I): I ≈ 0.705A.
      • Power Factor (PF): PF ≈ 0.563.
      • Power Consumed (P): P ≈ 98.95W.
      • Voltage across Components:
        • Voltage across Resistor (VR) ≈ 141V.
        • Voltage across Inductor (VL) ≈ 17.72V.
        • Voltage across Capacitor (VC) ≈ 224.41V.

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    Description

    This quiz covers the concepts of single phase AC circuits as outlined in Unit 3. You will explore important definitions such as amplitude, one full cycle, and instantaneous value. Test your understanding of these key terms and their significance in alternating current systems.

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