30 Questions
What is the method used to find the effective value of a harmonic quantity?
Taking the square root of the sum of squared rms values
In the context of phasors, what does it mean when two phasors are in phase?
The phase angle between them is zero
Which component should be squared when finding the RMS value of a harmonic quantity?
Amplitude
How are phasors used to represent sinusoidal quantities?
By avoiding drawing sine waves
What do phasors represent in relation to sinusoidal quantities?
The amplitude
When two phasors are out of phase, what does the phase angle between them signify?
The rotation needed to align them
What is the total resistance of a circuit with resistors 2Ω, 4Ω, and 6Ω in parallel?
7Ω
Which resistors are in parallel in a circuit with resistors of 1Ω, 3Ω, and 5Ω?
1Ω and 3Ω and 5Ω
What is the total resistance of a circuit with resistors of 1Ω and 2Ω in series, and this combination in parallel with a 3Ω resistor?
5/6 Ω
In a circuit with resistors of 2Ω, 4Ω, 6Ω, and 8Ω, which pairs are in series?
2Ω & 4Ω, 6Ω & 8Ω
What is the total resistance of a circuit with resistors of 2Ω, 3Ω, and 4Ω in series followed by a parallel connection with a resistor of 5Ω?
$\frac{82}{37}$ Ω
Which rule is applied to distribute current between parallel branches in a circuit?
Current Division Rule
What is the purpose of a phasor diagram in network analysis?
To display magnitude and phase relations among various quantities in the network
In a circuit where the current lags the voltage by 30°, what does this indicate?
The circuit contains inductive components
How can the addition of sinusoidal quantities be represented in a phasor diagram?
By performing vector sum of their phasors
What must be done to subtract a sinusoidal quantity from another in a phasor diagram?
Reverse the subtracted quantity and add it as a vector to the other phasors
What happens when 180° is added to the angle of a sinusoidal quantity?
It inverts and reverses the phase of the quantity
Under what condition can sinusoidal quantities be added or subtracted?
They must have the same frequency
What is the reactance of the coil?
31.416 ohms
In the given circuit, what is the impedance?
33.630 ohms
What is the current in the circuit?
2.974 A
Calculate the phase angle between the current and the applied voltage.
64.23 degrees
In Example 2, what is the capacitance required for the given circuit?
115 μF
What is another name for Active Power in AC circuits?
Actual Power
What is the root mean square value of a sine wave with a peak value of Vm?
$\frac{2Vm}{3}$
What is the total area under a sine wave from 0 to 2π?
$\frac{5Vm\pi}{2}$
What is the expression for the voltage in an ac generator in terms of peak voltage and angular frequency?
$V_m \sin(\omega t)$
What is the peak current expression for current in terms of peak current and frequency in an ac generator?
$I_m \sin(2\pi ft)$
What does the angular frequency specify in ac generators?
Number of cycles per unit time
What is the formula for calculating the area under a squared right-angled triangular wave?
$\frac{1}{2}bh$
Study Notes
Harmonics and RMS Values
- An even multiple of the fundamental is an even harmonic.
- The effective value of a harmonic quantity is obtained by:
- First, obtaining the square of the RMS value of each term.
- Adding the obtained squared RMS values.
- Taking the square root of the sum.
Phasors
- Phasors are used to represent sinusoidal quantities to avoid drawing sine waves.
- A phasor is a straight line whose length is proportional to the RMS voltage or current it represents.
- Phasors bear an arrow to show the phase angle or phase displacement between voltages and currents.
Phasors in Phase and Out of Phase
- Two phasors are said to be in phase when they point in the same direction.
- The phase angle between them is then zero.
- Two phasors are said to be out of phase when they point in different directions.
- The phase angle between them is the angle through which one of them has to be rotated to make it point in the same direction as the other.
Resistors in Parallel
- The total resistance RT is given by: 1/RT = 1/R1 + 1/R2.
- Effective circuit resistance is found by identifying and putting together series and/or parallel resistors.
Effective Resistance of a Circuit
- Examples of finding the total resistance of a circuit are provided, including circuits with multiple resistors in parallel and series.
Current Division Rule
- The current division rule is applied to share current between parallel branches.
- The rule is used to find the current in each branch.
Phasor Diagrams
- Phasor diagrams are used to show the magnitude and phase relations among the various quantities within a network.
- Phasor diagrams are often helpful in the analysis of the network.
Addition and Subtraction of Sinusoidal Quantities
- The sum of sinusoidal quantities is obtained by taking the vector sum of their phasors.
- The difference of sinusoidal quantities is obtained by first reversing the subtracted quantity and adding it as a vector to the other phasors.
- A sinusoidal quantity is reversed by adding 180° to its angle.
- Only sinusoidal quantities of the same frequency can be added or subtracted.
Impedance (Z)
- The impedance of a circuit is a measure of the total opposition to current flow.
- Examples of finding the impedance of a circuit are provided, including circuits with resistors, capacitors, and inductors.
Power in AC Circuits
- There are three kinds of power in ac circuits:
- Apparent Power (S) measured in Volt-amperes (VA).
- Active Power (P) measured in Watts (W).
- Reactive Power (Q) measured in Volt-amperes reactive (VAR).
Root Mean Square (RMS) Value
- The RMS value is the square root of the mean of the squared values.
- The RMS value is used to calculate the effective value of a sinusoidal quantity.
- The RMS value is used to calculate the power in an AC circuit.
Sinusoidal Voltages and Currents
- Voltages and currents of commercial ac generators have the following expressions:
- v = Vm sin ωt or v = Vm sin 2πft.
- i = Im sin ωt or i = Im sin 2πft.
- The peak voltage Vm and peak current Im are the maximum values of the voltage and current, respectively.
Test your understanding of resistors in parallel by identifying which resistors are connected in parallel in a circuit. Calculate the total resistance when resistors are in parallel. Determine the effective resistance of a circuit by combining series and parallel resistors.
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