AC Circuit Analysis: Resistor
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Questions and Answers

What is the primary purpose of the Root-Mean-Square (r.m.s.) value?

  • To calculate the mean rate of heat produced by an alternating current (correct)
  • To measure the peak value of an alternating current
  • To measure the average voltage of an alternating current
  • To determine the frequency of an alternating current

    • What is the relationship between the peak current and the r.m.s. current?

  • I_rms = I_o * sqrt(2)
  • I_rms = I_o
  • I_rms = I_o / 2
  • I_rms = I_o / sqrt(2) (correct)

    • If an AC voltmeter reads 220Vrms, what is the maximum voltage?

  • 440V
  • 311V (correct)
  • 220V
  • 400V

    • What is the equation for the instantaneous voltage in an AC circuit?

    <p>V(t) = V_o sin(ωt)</p> Signup and view all the answers

    If an AC ammeter reads 2A in a circuit with a 20Ω resistor, what is the voltage across the resistor?

    <p>60V</p> Signup and view all the answers

    If a 40Ω resistor is connected across a 15Vrms variable-frequency AC power source, what is the current flowing through the resistor?

    <p>375mA rms</p> Signup and view all the answers

    If an AC voltage is given by V = 60 sin(120πt) volts, what is the frequency of the voltage?

    <p>60 Hz</p> Signup and view all the answers

    If a 40Ω resistor is connected across a 15Vrms variable-frequency AC power source, what is the power consumed by the resistor?

    <p>5.625 W</p> Signup and view all the answers

    What is the expression for the phase angle φ in a circuit?

    <p>tan φ = VR / (XL - XC)</p> Signup and view all the answers

    If XL > XC, what is the nature of the circuit?

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

    What is the expression for voltage in an inductive circuit?

    <p>v(t) = V0 sin (ωt - φ)</p> Signup and view all the answers

    What is the expression for current in a capacitive circuit?

    <p>i(t) = I0 sin (ωt + φ)</p> Signup and view all the answers

    What is the unit of inductance?

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

    What is the unit of capacitance?

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

    What is the relationship between XL and XC in a capacitive circuit?

    <p>XL &lt; XC</p> Signup and view all the answers

    What is the term for the combination of real power and reactive power?

    <p>Apparent power</p> Signup and view all the answers

    What is the formula to calculate the reactance of a capacitor?

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

    What is the voltage across the capacitor when the current is maximum?

    <p>0</p> Signup and view all the answers

    What is the expression for the voltage across the capacitor with respect to time?

    <p>VC(t) = V0 sin(ωt - 90°)</p> Signup and view all the answers

    What is the current flowing through a capacitor when connected to a 120-V AC voltage source with a frequency of 60 Hz, if the capacitor has a capacitance of 20 μF?

    <p>1.13 A</p> Signup and view all the answers

    What is the value of current flowing through a 0.3-μF capacitor when connected to a 15-V variable-frequency AC power source with a frequency of 100 Hz?

    <p>0.47 A</p> Signup and view all the answers

    What is the reactance of a 4-μF capacitor connected to an alternating current line with a frequency of 500 Hz?

    <p>79.58 Ω</p> Signup and view all the answers

    In a R-L-C series circuit, what is the expression for the total voltage VT?

    <p>VT = IZ</p> Signup and view all the answers

    What is the voltage drop across the terminals of a 4-μF capacitor when connected to an alternating current line with a frequency of 500 Hz and a current of 30 mA?

    <p>12.67 V</p> Signup and view all the answers

    What is the impedance Z of a R-L-C series circuit?

    <p>Z = √(R2 + XL2 - XC2)</p> Signup and view all the answers

    What is the phase angle φ in a R-L-C series circuit?

    <p>The angle between the total voltage and the current I</p> Signup and view all the answers

    What is the expression for the current flowing through a capacitor with respect to time?

    <p>I(t) = I0 sin(ωt)</p> Signup and view all the answers

    In a R-L-C series circuit, what can be the sign of the phase angle φ?

    <p>Either positive or negative</p> Signup and view all the answers

    What is the expression for the voltage across the resistor VR?

    <p>VR = IR</p> Signup and view all the answers

    What is the inductive reactance XL?

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

    What is the total voltage VT in a R-L-C series circuit when VL = VC?

    <p>VT = VR</p> Signup and view all the answers

    What is the condition for the total voltage VT to be maximum in a R-L-C series circuit?

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

    What is the unit of measurement for resistance?

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

    What is the formula for the instantaneous current flowing through a resistor in an AC circuit?

    <p>i(t) = V0 sin(ωt)/R</p> Signup and view all the answers

    What is the relationship between current and voltage in an AC circuit through a pure resistor?

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

    What is the formula for inductive reactance?

    <p>XL = 2πfL</p> Signup and view all the answers

    What is the phase angle between the current and voltage in an AC circuit through a pure inductor?

    <p>-90°</p> Signup and view all the answers

    What is the formula for the instantaneous current flowing through an inductor in an AC circuit?

    <p>i(t) = V0 sin(ωt - 90°)/XL</p> Signup and view all the answers

    What is the peak or maximum current in an AC circuit through a resistor?

    <p>Io = V0/R</p> Signup and view all the answers

    What is the relationship between the voltage and current in an AC circuit through a pure inductor?

    <p>Voltage leads current by 90°</p> Signup and view all the answers

    What is the unit of measurement for inductive reactance?

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

    What is the formula for the voltage across a resistor in an AC circuit?

    <p>V(t) = i(t)R</p> Signup and view all the answers

    Study Notes

    AC Through a Pure Resistor

    • A resistor offers resistance to the flow of current, measured in ohms (Ω)
    • The instantaneous current flowing through the circuit is I(t) = V(t) / R
    • The voltage and current are in phase

    AC Through a Pure Inductor

    • The instantaneous current through the inductor is I(t) = -I₀ sin(ωt - 90°)
    • The inductive reactance is XL = ωL
    • The current lags the voltage by 90°

    Root-Mean-Square (RMS) Values

    • RMS values of voltage and current are the values that produce the same heating effect as the AC voltage
    • RMS values are calculated as I₀ / √2 and V₀ / √2
    • Ammeters and voltmeters measure RMS values

    Relationship Between Peak and RMS Values

    • The relationship between peak and RMS values is I₀ = √2 I_rms and V₀ = √2 V_rms

    Examples

    • Examples include determining maximum voltage, peak current, and RMS values, and calculating current and voltage in various AC circuits

    Capacitors in AC Circuits

    • The voltage equation across the capacitor is V(t) = V₀ sin(ωt)
    • The current equation through the capacitor is I(t) = I₀ sin(ωt - 90°)
    • The capacitive reactance is XC = 1 / ωC
    • The current leads the voltage by 90°

    R-L-C Series Circuit

    • The impedance of the circuit is Z = √(R² + (XL - XC)²)
    • The phase angle between the total voltage and the current is tan(φ) = (XL - XC) / R
    • The circuit can be inductive (XL > XC) or capacitive (XL < XC)

    Examples - "F"

    • Examples include determining current, voltage, and reactance in various AC circuits

    Examples - "I"

    • Examples include determining impedance, current, voltage, power, and power factor in various AC circuits

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    Description

    Understand how resistors behave in AC circuits, including the relationship between voltage and current, and the concept of phase.

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