Quick recall · 129 cards
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In a parallel combination of conductances G1 = 4 ℧ and G2 = 8 ℧, what is the equivalent conductance GT?
A · A) 12 ℧
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The resistivity of an ideal conductor is:
B · B) Nearly zero
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Find the value of the currents I1, I2 and I3 flowing clockwise in the first, second and third mesh respectively.
A · I1= 1.54A, I2=-0.189A, I3= -1.195A
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Find the value of the currents I1 and I2 flowing clockwise in the first and second mesh respectively.
D · -0.96A, -1.73A
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"Maximum power output is obtained from a network when the load resistance is equal to the output resistance of the network as seen from the terminals of the load". The above statement is associated with
D · Maximum power transfer theorem
PYQ · 2024
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All the elements in the circuit are ideal. The power delivered by the 10 V source in watts is
A · 0
PYQ · 2024
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The circuit shown in the figure with the switch S open, is in steady state. After the switch S is closed, the time constant of the circuit in seconds is
A · 1.25
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An R-C series AC circuit has resistance of 15 \( \Omega \) and capacitive reactance \( X_C \) of 15 \( \Omega \). If it is connected to an AC voltage source, the phase angle between voltage and current will be:
C · 45°
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A parallel R-L-C circuit is working at its resonant frequency. Which of the following statements is/are correct?
B · (b) The current in the circuit is minimum.
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In the case of a three-phase system with an unbalanced load, which of the following is correct?
C · C. The line voltages are equal
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Which topology has a single point of failure?
B · Star
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Which topology requires the highest number of cables and ports?
D · Mesh
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A network topology where each node connects to a central switching device is known as
D · Star
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Which type of network topology provides the highest level of redundancy?
B · Mesh
**Mesh topology** offers highest redundancy with multiple paths between nodes. If one link fails, alternate paths exist. Ring has one backup path, star fails at center, bus fails at break.[3]
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A short-circuit admittance matrix of a two-port network is \[ \begin{bmatrix} 0 & -\frac{1}{2} \\ \frac{1}{2} & 0 \end{bmatrix} \]. Which of the following statements is TRUE about this network?
B · B) It is reciprocal but not symmetrical
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Which of the following best defines electrical resonance?
A · The condition where inductive reactance equals capacitive reactance
Electrical resonance occurs when the inductive reactance equals the capacitive reactance, causing the circuit to oscillate at its natural frequency.
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Which type of resonance occurs when the impedance of the circuit is minimum and current is maximum?
B · Series resonance
In series resonance, the impedance is minimum and current is maximum at the resonant frequency.
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Which of the following is NOT a type of resonance in electrical circuits?
D · Thermal resonance
Thermal resonance is not a recognized type of resonance in electrical circuits, unlike series, parallel, and magnetic resonance.
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Refer to the diagram below of a series RLC circuit. What is the resonant frequency \( f_0 \) of the circuit?
A · \( \frac{1}{2\pi\sqrt{LC}} \)
The resonant frequency for a series RLC circuit is given by \( f_0 = \frac{1}{2\pi\sqrt{LC}} \).
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In a series resonance circuit, which of the following statements is TRUE at resonance?
B · Voltage across L and C are equal and out of phase
At resonance, the voltages across the inductor and capacitor are equal in magnitude but 180° out of phase, causing them to cancel each other.
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Calculate the quality factor \( Q \) of a series RLC circuit with \( R = 10\ \Omega \), \( L = 0.1\ H \), and \( C = 10\ \mu F \).
A · 31.62
Quality factor \( Q = \frac{1}{R} \sqrt{\frac{L}{C}} = \frac{1}{10} \sqrt{\frac{0.1}{10 \times 10^{-6}}} = 31.62 \).
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Refer to the diagram below of a parallel RLC circuit. What happens to the impedance at the resonant frequency?
B · Impedance is maximum
In a parallel resonance circuit, the impedance is maximum at the resonant frequency because the inductive and capacitive currents cancel each other.
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In a parallel resonance circuit, the current drawn from the source at resonance is:
B · Minimum
At resonance in a parallel circuit, the total current drawn from the source is minimum because the inductive and capacitive branch currents cancel each other.
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Calculate the resonant frequency \( f_0 \) of a parallel RLC circuit with \( L = 25\ mH \) and \( C = 100\ nF \).
A · 31.83 kHz
Resonant frequency \( f_0 = \frac{1}{2\pi\sqrt{LC}} = \frac{1}{2\pi\sqrt{25 \times 10^{-3} \times 100 \times 10^{-9}}} = 31.83 \text{ kHz} \).
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Refer to the frequency response graph below of a resonant circuit. What does the bandwidth \( BW \) represent?
A · The frequency range where power is at least half of maximum
Bandwidth is the frequency range over which the power is at least half (or the voltage/current amplitude is \( \frac{1}{\sqrt{2}} \) of the maximum), defining the selectivity of the circuit.
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The quality factor \( Q \) of a resonant circuit is related to bandwidth \( BW \) and resonant frequency \( f_0 \) by which formula?
A · \( Q = \frac{f_0}{BW} \)
Quality factor \( Q \) is the ratio of resonant frequency to bandwidth, \( Q = \frac{f_0}{BW} \), indicating the sharpness of resonance.
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Refer to the bandwidth illustration graph below. If the resonant frequency \( f_0 = 1\ MHz \) and bandwidth \( BW = 20\ kHz \), what is the quality factor \( Q \)?
A · 50
Quality factor \( Q = \frac{f_0}{BW} = \frac{1,000,000}{20,000} = 50 \). However, since 1 MHz / 20 kHz = 50, correct answer is 50, option A. (Correcting answer accordingly.)
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Which of the following is a common application of resonance in electrical circuits?
A · Tuning radio receivers
Resonance is widely used in tuning radio receivers to select desired frequencies by adjusting the resonant frequency of the circuit.
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In a series RLC circuit, at resonance, which of the following statements is TRUE?
A · The inductive reactance equals the capacitive reactance
At resonance in a series RLC circuit, inductive reactance (X_L) equals capacitive reactance (X_C), resulting in the circuit's impedance being purely resistive and minimum.
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Refer to the diagram below of a series RLC circuit. If \( R = 10\ \Omega \), \( L = 50\ mH \), and \( C = 20\ \mu F \), what is the resonant frequency \( f_0 \)?
C · \( 1591.55\ Hz \)
Resonant frequency \( f_0 = \frac{1}{2\pi\sqrt{LC}} = \frac{1}{2\pi\sqrt{50\times10^{-3} \times 20\times10^{-6}}} \approx 1591.55\ Hz \).
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Which of the following best describes the current behavior in a parallel resonance circuit at resonance?
A · Current is minimum and voltage is maximum
At parallel resonance, the circuit draws minimum current from the source while the voltage across the circuit is maximum due to high impedance.
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Refer to the frequency response graph below of a parallel RLC circuit. What does the peak of the curve represent?
A · Resonant frequency where impedance is maximum
In a parallel RLC circuit, the peak of the frequency response graph corresponds to the resonant frequency where the circuit impedance is maximum.
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In a parallel RLC circuit, which of the following affects the bandwidth of the resonance curve?
C · The resistance value
In a parallel RLC circuit, the resistance affects the bandwidth; higher resistance results in narrower bandwidth and higher selectivity.
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Calculate the resonant frequency \( f_0 \) of a circuit with \( L = 25\ mH \) and \( C = 100\ nF \).
D · \( 50.3\ kHz \)
Resonant frequency \( f_0 = \frac{1}{2\pi\sqrt{LC}} = \frac{1}{2\pi\sqrt{25\times10^{-3} \times 100\times10^{-9}}} \approx 50.3\ kHz \).
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Which of the following statements about the quality factor (Q) of a resonant circuit is CORRECT?
B · Q is inversely proportional to bandwidth
Quality factor (Q) is inversely proportional to bandwidth; higher Q means narrower bandwidth and better selectivity.
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Refer to the frequency response graph below. If the bandwidth \( BW \) is the frequency range between \( f_1 \) and \( f_2 \), what does the selectivity of the circuit depend on?
D · The ratio \( \frac{f_0}{BW} \)
Selectivity is defined as the ratio of resonant frequency \( f_0 \) to bandwidth \( BW \), indicating how well the circuit discriminates between frequencies.
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Which of the following is a common application of resonance in electrical circuits?
B · Frequency selection in radio receivers
Resonance is widely used for frequency selection in radio receivers to tune to desired signals.
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In a series RLC circuit, increasing the resistance \( R \) will have which effect on the resonance characteristics?
B · Decrease the quality factor and widen the bandwidth
Increasing resistance decreases the quality factor (Q), resulting in a wider bandwidth and less sharp resonance.
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Refer to the phasor diagram below of a series RLC circuit at resonance. Which phasor represents the voltage across the inductor?
A · Phasor A (leading current by 90°)
The voltage across the inductor leads the current by 90°, represented by Phasor A in the diagram.
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Given a series RLC circuit with \( R = 10\ \Omega \), \( L = 100\ mH \), and \( C = 10\ \mu F \), calculate the bandwidth \( BW \) if the quality factor \( Q \) is \( 31.8 \). Use \( BW = \frac{f_0}{Q} \).
A · \( 50\ Hz \)
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Which of the following is NOT a basic type of network topology in electrical circuits?
C · Mesh topology
Mesh topology is a network analysis method, not a basic type of network topology like series, parallel, or star.
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In a star topology, how many branches connect to the central node?
C · Three or more
In star topology, three or more branches connect to a central node, forming a star-like structure.
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Which statement best describes the difference between series and parallel connections in electrical networks?
B · In series, current is the same through components; in parallel, voltage is the same.
In series connections, current is the same through all components, while voltage divides. In parallel connections, voltage is the same across components, while current divides.
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Refer to the diagram below showing a simple network graph. How many nodes and branches are present in the network?
B · 4 nodes, 4 branches
The diagram shows 4 nodes connected by 4 branches forming a network graph.
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In graph theory applied to electrical networks, what is the definition of a 'tree'?
A · A subgraph containing all nodes with no closed loops
A tree is a subgraph that includes all nodes but contains no closed loops, used for network analysis.
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Which of the following correctly describes the relationship between the number of branches (b), nodes (n), and independent loops (l) in a planar network graph?
A · l = b - n + 1
The formula \( l = b - n + 1 \) gives the number of independent loops in a planar network graph.
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Refer to the circuit diagram below. What is the equivalent resistance between points A and B if resistors R1 and R2 are connected as shown?
B · \( R_{eq} = \frac{R_1 R_2}{R_1 + R_2} \)
The resistors R1 and R2 are connected in parallel; hence the equivalent resistance is given by \( \frac{R_1 R_2}{R_1 + R_2} \).
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Which of the following statements is TRUE for resistors connected in series?
D · The total resistance is the sum of individual resistances.
In series connection, the total resistance is the sum of individual resistances, and current is the same through each resistor.
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In mesh analysis, what is the primary variable solved for in each mesh of a planar circuit?
C · Mesh current
Mesh analysis involves solving for mesh currents, which are hypothetical currents circulating around the loops of the circuit.
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Refer to the circuit diagram below with two meshes. If mesh currents \( I_1 \) and \( I_2 \) are defined as shown, which of the following equations correctly represents the KVL for mesh 1?
A · \( R_1 I_1 + R_3 (I_1 - I_2) = V_s \)
For mesh 1, the voltage drops across R1 and R3 are \( R_1 I_1 \) and \( R_3 (I_1 - I_2) \) respectively, summing to the source voltage \( V_s \).
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Which of the following is a key advantage of nodal analysis over mesh analysis in electrical circuits?
A · It requires fewer equations for circuits with many nodes and fewer meshes.
Nodal analysis is often more efficient for circuits with many meshes but fewer nodes, as it requires fewer simultaneous equations.
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Refer to the star-delta transformation diagram below. If the star resistances are \( R_1, R_2, R_3 \), which of the following gives the equivalent delta resistance \( R_{ab} \)?
A · \( R_{ab} = \frac{R_1 R_2 + R_2 R_3 + R_3 R_1}{R_3} \)
The delta resistance between nodes a and b is given by \( \frac{R_1 R_2 + R_2 R_3 + R_3 R_1}{R_3} \) in star-delta transformation.
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Which of the following is the correct formula to convert delta resistances \( R_{ab}, R_{bc}, R_{ca} \) to star resistances \( R_1, R_2, R_3 \)?
A · \( R_1 = \frac{R_{ab} R_{ca}}{R_{ab} + R_{bc} + R_{ca}} \)
The star resistance \( R_1 \) is calculated as \( \frac{R_{ab} R_{ca}}{R_{ab} + R_{bc} + R_{ca}} \) when converting from delta to star.
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Refer to the star and delta network diagram below. If the star resistances are \( R_1 = 2 \Omega, R_2 = 3 \Omega, R_3 = 6 \Omega \), what is the value of the delta resistance \( R_{ab} \)?
A · 6 \( \Omega \)
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Which of the following best defines a 'node' in an electrical network?
A · A point where two or more circuit elements are connected
A node is defined as a point in a circuit where two or more elements are connected.
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In network topology, what is the term used for a closed conducting path in a circuit?
C · Loop
A loop is a closed conducting path in a circuit.
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Which statement correctly describes a 'branch' in an electrical network?
B · A single element or a group of elements connected between two nodes
A branch is a single element or a group of elements connected between two nodes.
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Refer to the diagram below showing three resistors connected. Which topology does this circuit represent?
C · Series-Parallel
The circuit has some resistors in series and some in parallel, representing a series-parallel topology.
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Which of the following is true for resistors connected in parallel?
B · The voltage across each resistor is the same
In parallel connection, voltage across each resistor is the same.
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In the series-parallel circuit shown below, what is the equivalent resistance between points A and B?
B · 6 \( \Omega \)
By calculating series and parallel combinations, the equivalent resistance is 6 \( \Omega \).
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Which of the following topologies is the most suitable for minimizing the number of branches in a network graph?
C · Tree topology
A tree topology is a subgraph that connects all nodes without forming any loops, minimizing branches.
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In graph theory applied to electrical circuits, what does the term 'tree' refer to?
B · A subgraph connecting all nodes without any loops
A tree is a subgraph that connects all nodes without forming any loops.
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Refer to the graph representation below. How many loops are present in this network?
B · 2
The graph contains two independent loops as shown by the closed paths.
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Which of the following statements about branches and loops in a network graph is correct?
A · Number of loops = Number of branches - Number of nodes + 1
The formula for the number of independent loops is \( b - n + 1 \), where \( b \) is branches and \( n \) is nodes.
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Refer to the circuit diagram below. Applying delta-wye transformation, what is the equivalent resistance between terminals A and B?
B · 6 \( \Omega \)
Using delta-wye formulas, the equivalent resistance is 6 \( \Omega \) between terminals A and B.
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Which of the following is NOT a correct step in performing a delta-to-wye transformation?
C · Replace the delta network with three resistors connected in a triangle
Replacing the delta with three resistors connected in a triangle is the original delta configuration, not the wye transformation.
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Refer to the circuit below. After applying wye-delta transformation, what is the new resistance value replacing the wye network?
D · 7 \( \Omega \)
Using wye-delta formulas, the equivalent delta resistor is 7 \( \Omega \).
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Which of the following is a primary application of network topology in electrical circuit analysis?
B · To simplify complex circuits for easier analysis
Network topology helps in simplifying complex circuits by identifying series, parallel, and other connections.
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Refer to the circuit below. Using network topology concepts, which method would be most effective to find the current through resistor R3?
C · Delta-wye transformation followed by series-parallel reduction
Delta-wye transformation simplifies the network, making it easier to analyze current through R3.
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Which of the following best describes the role of network topology in fault analysis of electrical circuits?
A · It helps in identifying the location and nature of faults by analyzing connectivity and loops
Network topology analysis helps locate faults by studying the connectivity and loops in the circuit.
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Which of the following best defines a two port network?
B · A network with two pairs of terminals for input and output
A two port network is defined as an electrical network with two pairs of terminals, one pair for input and one pair for output, allowing analysis of input-output relationships.
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Which of the following is NOT a basic parameter of a two port network?
D · Power factor
Power factor is not a basic two port network parameter. Basic parameters include input impedance, output admittance, voltage gain, current gain, etc.
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Which of the following statements about two port network parameters is TRUE?
D · All of the above
Z-parameters relate voltages to currents, Y-parameters relate currents to voltages, and h-parameters are hybrid parameters combining voltage and current variables.
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Refer to the diagram below of a two port network with Z-parameters. If \( I_2 = 0 \), the input impedance \( Z_{in} \) is given by which of the following?
A · \( Z_{in} = Z_{11} \)
When \( I_2 = 0 \) (output port open-circuited), the input impedance equals \( Z_{11} \) by definition of Z-parameters.
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Which of the following is the correct expression for \( Z_{21} \) in terms of two port network voltages and currents?
A · \( Z_{21} = \frac{V_2}{I_1} \text{ with } I_2=0 \)
By definition, \( Z_{21} = \frac{V_2}{I_1} \) when \( I_2 = 0 \) (output port open-circuited).
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Refer to the diagram below of a two port network with Y-parameters. If \( V_2 = 0 \), what is the input admittance \( Y_{in} \)?
A · \( Y_{in} = Y_{11} \)
When \( V_2 = 0 \) (output port short-circuited), the input admittance equals \( Y_{11} \) by definition of Y-parameters.
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Given a two port network with Y-parameters \( Y_{11} = 5mS, Y_{12} = -2mS, Y_{21} = -2mS, Y_{22} = 4mS \), calculate the input admittance \( Y_{in} \) when the output port is open-circuited (\( I_2 = 0 \)).
B · \( 5mS - \frac{(-2mS)(-2mS)}{4mS} = 4mS \)
Input admittance with output open is \( Y_{in} = Y_{11} - \frac{Y_{12} Y_{21}}{Y_{22}} = 5mS - \frac{4mS}{4mS} = 4mS \).
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Which of the following correctly expresses \( Y_{12} \) in terms of two port network voltages and currents?
A · \( Y_{12} = \frac{I_1}{V_2} \text{ with } V_1=0 \)
By definition, \( Y_{12} = \frac{I_1}{V_2} \) when \( V_1 = 0 \) (input port short-circuited).
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Which of the following is NOT a characteristic of hybrid (h) parameters in two port networks?
C · They are symmetrical in reciprocal networks
Hybrid parameters are generally not symmetrical even in reciprocal networks; symmetry applies to Z and Y parameters but not necessarily to h-parameters.
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Given the hybrid parameter equations \( V_1 = h_{11} I_1 + h_{12} V_2 \) and \( I_2 = h_{21} I_1 + h_{22} V_2 \), what are the units of \( h_{12} \)?
C · Dimensionless
\( h_{12} \) relates \( V_1 \) to \( V_2 \) and is a voltage ratio, so it is dimensionless.
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Refer to the diagram below of a two port network with given h-parameters. If \( I_2 = 0 \), what is the input impedance \( Z_{in} \) in terms of h-parameters?
A · \( Z_{in} = h_{11} \)
When \( I_2 = 0 \) (output port open), input impedance equals \( h_{11} \) by definition.
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Given the h-parameters \( h_{11} = 50\Omega, h_{12} = 0.01, h_{21} = 100, h_{22} = 0.02S \), calculate the output admittance \( Y_{out} \) when \( I_1 = 0 \).
A · \( Y_{out} = h_{22} = 0.02S \)
Output admittance with \( I_1=0 \) equals \( h_{22} \) by definition.
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Refer to the diagram below of a two port network with ABCD parameters. If \( V_2 = 10V \) and \( I_2 = 2A \), and \( A=1.5, B=20\Omega, C=0.1S, D=2 \), what is the input voltage \( V_1 \)?
A · \( V_1 = A V_2 + B (-I_2) = 1.5 \times 10 - 20 \times 2 = -25V \)
Using \( V_1 = A V_2 + B (-I_2) = 1.5 \times 10 - 20 \times 2 = 15 - 40 = -25V \).
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Which of the following conditions must be satisfied for a two port network to be reciprocal?
A · \( Z_{12} = Z_{21} \) or \( Y_{12} = Y_{21} \)
Reciprocity requires the off-diagonal parameters to be equal: \( Z_{12} = Z_{21} \) or \( Y_{12} = Y_{21} \).
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For a two port network, symmetry implies which of the following?
A · \( Z_{11} = Z_{22} \) and \( Z_{12} = Z_{21} \)
Symmetry requires the diagonal parameters to be equal and the off-diagonal parameters to be equal, e.g., \( Z_{11} = Z_{22} \) and \( Z_{12} = Z_{21} \).
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Which of the following is TRUE for a reciprocal and symmetrical two port network in terms of ABCD parameters?
B · \( A = D \) and \( B = C \)
For reciprocal and symmetrical networks, \( A = D \) and \( B = C \) in ABCD parameters.
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Which of the following is the correct conversion formula from Z-parameters to Y-parameters for a two port network?
A · \( [Y] = [Z]^{-1} \)
Y-parameters are the inverse of Z-parameters matrix: \( [Y] = [Z]^{-1} \).
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Given the Z-parameter matrix \( \begin{bmatrix} 4 & 2 \\ 2 & 3 \end{bmatrix} \), what is the corresponding Y-parameter \( Y_{11} \)?
A · \( \frac{3}{8} = 0.375 S \)
Y-parameters are inverse of Z matrix. \( Y_{11} = \frac{Z_{22}}{det(Z)} = \frac{3}{(4 \times 3 - 2 \times 2)} = \frac{3}{8} = 0.375 S \).
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Refer to the diagram below showing two cascaded two port networks with ABCD parameters \( [A_1,B_1,C_1,D_1] \) and \( [A_2,B_2,C_2,D_2] \). What is the overall ABCD parameter matrix of the cascaded network?
A · \( [A,B,C,D] = [A_1,B_1,C_1,D_1] \times [A_2,B_2,C_2,D_2] \)
The overall ABCD matrix of cascaded two port networks is the matrix product of individual ABCD matrices in order: \( [A,B,C,D] = [A_1,B_1,C_1,D_1] \times [A_2,B_2,C_2,D_2] \).
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If two two port networks with ABCD parameters \( [A_1,B_1,C_1,D_1] \) and \( [A_2,B_2,C_2,D_2] \) are cascaded, which of the following is the expression for the overall parameter \( B \)?
A · \( B = A_1 B_2 + B_1 D_2 \)
Overall \( B \) parameter is computed as \( B = A_1 B_2 + B_1 D_2 \) in the matrix multiplication of ABCD parameters.
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Which of the following is a common application of two port networks in electrical engineering?
D · All of the above
Two port networks are widely used to model amplifiers, analyze transmission lines, and design filters among other applications.
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Refer to the diagram below showing a two port network used as an amplifier with gain \( h_{21} = 100 \). If the input current \( I_1 = 1mA \), what is the output current \( I_2 \) assuming \( V_2 = 0 \)?
A · \( I_2 = 100mA \)
Output current \( I_2 = h_{21} I_1 = 100 \times 1mA = 100mA \).
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Which of the following is TRUE about cascading two port networks?
B · Overall ABCD parameters are the product of individual ABCD matrices
When two port networks are cascaded, their overall ABCD parameters are obtained by multiplying their individual ABCD matrices.
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Which of the following is a correct statement about interconversion of parameter sets for two port networks?
D · All of the above
All these interconversions are possible and commonly used in two port network analysis.
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Refer to the diagram below showing a two port network with given Z-parameters. If \( Z_{11} = 6\Omega, Z_{12} = 3\Omega, Z_{21} = 3\Omega, Z_{22} = 4\Omega \), what is the Y-parameter \( Y_{22} \)?
B · \( \frac{Z_{22}}{Z_{11} Z_{22} - Z_{12} Z_{21}} = \frac{4}{(6 \times 4 - 3 \times 3)} = 0.267 S \)
The Y-parameter \( Y_{22} = \frac{Z_{11}}{det(Z)} = \frac{4}{(6 \times 4 - 3 \times 3)} = 0.267 S \).
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Which of the following is a key advantage of using ABCD parameters in cascading two port networks?
A · They allow easy matrix multiplication to find overall parameters
ABCD parameters facilitate cascading by matrix multiplication, simplifying analysis of cascaded networks.
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Refer to the diagram below showing a two port network with given h-parameters. If \( h_{11} = 100\Omega, h_{12} = 0.02, h_{21} = 50, h_{22} = 0.04S \), calculate the input impedance \( Z_{in} \) when \( V_2 = 0 \).
B · \( Z_{in} = \frac{h_{11}}{1 - h_{12} h_{21}} = \frac{100}{1 - (0.02 \times 50)} = 200\Omega \)
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Which of the following statements about practical examples of two port networks is CORRECT?
A · Two port networks can model transformers, amplifiers, and filters
Two port networks are versatile models used for transformers, amplifiers, filters, and other practical circuits.
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Refer to the diagram below showing a two port network with given Y-parameters. If \( Y_{11} = 10mS, Y_{12} = -5mS, Y_{21} = -5mS, Y_{22} = 8mS \), calculate the output admittance \( Y_{out} \) when \( I_1 = 0 \).
B · \( Y_{out} = Y_{22} - \frac{Y_{12} Y_{21}}{Y_{11}} = 8mS - \frac{(-5mS)(-5mS)}{10mS} = 5.5mS \)
Output admittance with \( I_1=0 \) is \( Y_{out} = Y_{22} - \frac{Y_{12} Y_{21}}{Y_{11}} = 8mS - \frac{25mS^2}{10mS} = 5.5mS \).
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Which of the following is TRUE about the symmetry of two port networks in terms of h-parameters?
B · \( h_{11} = h_{22} \) and \( h_{12} = h_{21} \)
Symmetry in h-parameters requires \( h_{11} = h_{22} \) and \( h_{12} = h_{21} \).
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Refer to the diagram below showing a two port network with given ABCD parameters. If \( A = 1, B = 50\Omega, C = 0, D = 1 \), what type of network does this represent?
C · Series impedance
ABCD parameters with \( A = D = 1, C=0, B eq 0 \) represent a series impedance element.
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Which of the following is TRUE about the reciprocity condition for h-parameters in a two port network?
C · \( h_{12} = h_{21} \)
Reciprocity requires \( h_{12} = h_{21} \) for two port networks.
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Refer to the diagram below showing a two port network with Z-parameters. If the network is reciprocal and symmetrical, which of the following must be TRUE?
A · \( Z_{11} = Z_{22} \) and \( Z_{12} = Z_{21} \)
Reciprocal and symmetrical networks have equal diagonal and off-diagonal Z-parameters.
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Which of the following is the correct expression for the input impedance of a two port network in terms of Y-parameters when the output port is terminated with a load admittance \( Y_L \)?
A · \( Z_{in} = \frac{1}{Y_{11} - \frac{Y_{12} Y_{21}}{Y_{22} + Y_L}} \)
Input impedance with load admittance \( Y_L \) is given by \( Z_{in} = \frac{1}{Y_{11} - \frac{Y_{12} Y_{21}}{Y_{22} + Y_L}} \).
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Refer to the diagram below showing a two port network with given ABCD parameters. If the network is cascaded with an identical network, what is the overall \( A \) parameter?
A · \( A = A_1^2 \)
When two identical networks are cascaded, overall \( A = A_1 \times A_1 = A_1^2 \).
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Which of the following best defines a two port network?
B · A network with two pairs of terminals for input and output
A two port network is defined as an electrical network with two pairs of terminals, one pair for input and one pair for output, allowing analysis of input-output relationships.
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Which parameter set expresses the two port network equations as \( V_1 = Z_{11}I_1 + Z_{12}I_2 \) and \( V_2 = Z_{21}I_1 + Z_{22}I_2 \)?
B · Z-parameters
Z-parameters or impedance parameters relate port voltages to port currents using the given linear equations.
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Which of the following statements about h-parameters is TRUE?
C · They combine impedance and admittance parameters in a hybrid form.
h-parameters are hybrid parameters combining voltage and current variables in a mixed manner, unlike pure impedance or admittance parameters.
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Which parameter set is most suitable for analyzing cascade connections of two port networks?
D · ABCD-parameters
ABCD-parameters (transmission parameters) multiply directly for cascaded two port networks, simplifying analysis.
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Which condition must be satisfied for a two port network to be reciprocal?
A · \( Z_{12} = Z_{21} \)
Reciprocity requires the off-diagonal impedance parameters to be equal, i.e., \( Z_{12} = Z_{21} \).
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Refer to the diagram below of a symmetric two port network. Which of the following is TRUE about its Z-parameters?
A · \( Z_{11} = Z_{22} \) and \( Z_{12} = Z_{21} \)
Symmetry implies equal diagonal elements and reciprocity implies equal off-diagonal elements in the Z-parameter matrix.
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Which of the following is a typical application of two port networks?
B · Modeling amplifiers and filters
Two port networks are widely used to model amplifiers, filters, and other linear electrical circuits.
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Refer to the diagram below of a two port amplifier. If the input voltage is 2 V and the voltage gain is 10, what is the output voltage?
A · 20 V
Output voltage \( V_2 = \text{Gain} \times V_1 = 10 \times 2 = 20 \text{ V} \).
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Which of the following is a practical consideration when measuring two port network parameters?
C · Using matched loads to avoid reflections
Using matched loads during measurements avoids signal reflections and ensures accurate parameter determination.
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Which of the following correctly converts Z-parameters to Y-parameters for a two port network?
A · \( [Y] = [Z]^{-1} \)
Y-parameters are the inverse of Z-parameters, i.e., \( [Y] = [Z]^{-1} \).
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Which of the following statements about ABCD parameters is FALSE?
D · They cannot represent non-linear networks.
ABCD parameters are defined only for linear networks; they cannot represent non-linear networks, so the statement is TRUE, making option D false as a false statement.
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Refer to the diagram below of two two port networks connected in parallel. If their Y-parameters are \( [Y_1] \) and \( [Y_2] \), what is the Y-parameter matrix of the combined network?
A · \( [Y] = [Y_1] + [Y_2] \)
When two two port networks are connected in parallel, their admittance matrices add up.
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Which of the following parameter sets is dimensionally hybrid, involving both voltage and current ratios?
C · h-parameters
h-parameters are hybrid parameters involving voltage and current ratios, mixing impedance and admittance concepts.
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Refer to the diagram below of a two port network with Z-parameters \( Z_{11} = 8 \Omega, Z_{12} = 3 \Omega, Z_{21} = 3 \Omega, Z_{22} = 12 \Omega \). Which of the following statements is TRUE?
A · The network is reciprocal but not symmetric.
Since \( Z_{12} = Z_{21} = 3 \Omega \) and \( Z_{11} = 8 \Omega eq Z_{22} = 12 \Omega \), the network is reciprocal but not symmetric. So option A is correct.
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Which of the following is NOT a typical practical consideration when measuring two port network parameters?
C · Ignoring temperature effects
Ignoring temperature effects is not advisable as temperature can affect network parameters; it must be considered.
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Which of the following is TRUE about the determinant of the ABCD matrix for a reciprocal two port network?
B · It is always unity.
For reciprocal two port networks, the determinant of the ABCD matrix is always equal to 1.
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Refer to the diagram below of two two port networks connected in series. If their Z-parameters are \( [Z_1] \) and \( [Z_2] \), what is the Z-parameter matrix of the combined network?
A · \( [Z] = [Z_1] + [Z_2] \)
When two two port networks are connected in series, their impedance parameters add up.
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Which of the following is NOT a characteristic of reciprocal two port networks?
C · \( h_{12} = -h_{21} \)
For reciprocal networks, \( h_{12} = -h_{21} \) is generally NOT true; reciprocity implies \( h_{12} = h_{21} \) under certain conditions.
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Refer to the diagram below showing a two port network used as a filter. Which parameter set is most commonly used to analyze such frequency selective networks?
C · ABCD-parameters
ABCD-parameters are widely used in analyzing cascaded filters and transmission line networks.
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Which of the following is a correct statement about the measurement of two port parameters?
B · Y-parameters are measured with both ports short-circuited.
Y-parameters are measured by short-circuiting the ports appropriately to measure admittances.
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Which of the following is NOT true about interconversion between two port parameter sets?
C · ABCD parameters are always symmetric matrices.
ABCD parameters are not necessarily symmetric matrices; symmetry depends on network properties.
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Which of the following is TRUE about the series connection of two port networks in terms of Z-parameters?
A · The overall Z-parameters are the sum of individual Z-parameters.
In series connection, the overall impedance parameters add up.
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Which of the following is TRUE regarding the measurement of Z-parameters in a two port network?
A · Port 2 is open-circuited while measuring \( Z_{11} \) and \( Z_{21} \).
Z-parameters are measured by open-circuiting the output port (port 2) while applying signals to port 1.
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Which of the following is a key advantage of using ABCD parameters in two port network analysis?
B · They allow easy cascading of multiple two port networks.
ABCD parameters multiply directly when two port networks are cascaded, simplifying analysis of cascaded systems.
