42 Questions
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
What is the relationship between the peak current and the r.m.s. current?
I_rms = I_o / sqrt(2)
If an AC voltmeter reads 220Vrms, what is the maximum voltage?
311V
What is the equation for the instantaneous voltage in an AC circuit?
V(t) = V_o sin(ωt)
If an AC ammeter reads 2A in a circuit with a 20Ω resistor, what is the voltage across the resistor?
60V
If a 40Ω resistor is connected across a 15Vrms variable-frequency AC power source, what is the current flowing through the resistor?
375mA rms
If an AC voltage is given by V = 60 sin(120πt) volts, what is the frequency of the voltage?
60 Hz
If a 40Ω resistor is connected across a 15Vrms variable-frequency AC power source, what is the power consumed by the resistor?
5.625 W
What is the expression for the phase angle φ in a circuit?
tan φ = VR / (XL - XC)
If XL > XC, what is the nature of the circuit?
Inductive
What is the expression for voltage in an inductive circuit?
v(t) = V0 sin (ωt - φ)
What is the expression for current in a capacitive circuit?
i(t) = I0 sin (ωt + φ)
What is the unit of inductance?
Henry
What is the unit of capacitance?
Farad
What is the relationship between XL and XC in a capacitive circuit?
XL < XC
What is the term for the combination of real power and reactive power?
Apparent power
What is the formula to calculate the reactance of a capacitor?
XC = 1 / (2πfC)
What is the voltage across the capacitor when the current is maximum?
0
What is the expression for the voltage across the capacitor with respect to time?
VC(t) = V0 sin(ωt - 90°)
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?
1.13 A
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?
0.47 A
What is the reactance of a 4-μF capacitor connected to an alternating current line with a frequency of 500 Hz?
79.58 Ω
In a R-L-C series circuit, what is the expression for the total voltage VT?
VT = IZ
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?
12.67 V
What is the impedance Z of a R-L-C series circuit?
Z = √(R2 + XL2 - XC2)
What is the phase angle φ in a R-L-C series circuit?
The angle between the total voltage and the current I
What is the expression for the current flowing through a capacitor with respect to time?
I(t) = I0 sin(ωt)
In a R-L-C series circuit, what can be the sign of the phase angle φ?
Either positive or negative
What is the expression for the voltage across the resistor VR?
VR = IR
What is the inductive reactance XL?
The opposition to the current flow due to the inductor
What is the total voltage VT in a R-L-C series circuit when VL = VC?
VT = VR
What is the condition for the total voltage VT to be maximum in a R-L-C series circuit?
XL = XC
What is the unit of measurement for resistance?
Ohms
What is the formula for the instantaneous current flowing through a resistor in an AC circuit?
i(t) = V0 sin(ωt)/R
What is the relationship between current and voltage in an AC circuit through a pure resistor?
Current and voltage are in phase
What is the formula for inductive reactance?
XL = 2πfL
What is the phase angle between the current and voltage in an AC circuit through a pure inductor?
-90°
What is the formula for the instantaneous current flowing through an inductor in an AC circuit?
i(t) = V0 sin(ωt - 90°)/XL
What is the peak or maximum current in an AC circuit through a resistor?
Io = V0/R
What is the relationship between the voltage and current in an AC circuit through a pure inductor?
Voltage leads current by 90°
What is the unit of measurement for inductive reactance?
Ohms
What is the formula for the voltage across a resistor in an AC circuit?
V(t) = i(t)R
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
Understand how resistors behave in AC circuits, including the relationship between voltage and current, and the concept of phase.
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