Electrical Engineering Advanced Prep:
Master Circuit Analysis Practice Questions &
Detailed Explanations
Subject: Electrical Engineering - Advanced Circuit Analysis
Question 1: In a non-linear resistive network, the dynamic resistance $r_d$ is defined as the
slope of the voltage-current characteristic curve. If a device exhibits a characteristic defined by
$i = I_0(e^{v/V_T} - 1)$, determine the expression for dynamic conductance $g_d$ in terms of
current $i$.
A) $g_d = \frac{i}{V_T}$
B) $g_d = \frac{i + I_0}{V_T}$
C) $g_d = \frac{V_T}{i}$
D) $g_d = \frac{I_0}{V_T}e^{v/V_T}$
Correct Answer: B) $g_d = \frac{i + I_0}{V_T}$
Explanation: The dynamic conductance is $g_d = \frac{di}{dv}$. Given $i = I_0(e^{v/V_T} -
1)$, differentiating with respect to $v$ yields $\frac{di}{dv} = \frac{I_0}{V_T}e^{v/V_T}$. From
the original equation, $i + I_0 = I_0e^{v/V_T}$. Substituting this into the derivative expression,
we obtain $g_d = \frac{i + I_0}{V_T}$. Option A is incorrect as it neglects the saturation
current $I_0$.
Question 2: A two-port network is characterized by its $Z$-parameters. If the network is
reciprocal and symmetric, which of the following conditions must hold true for the $Z$-matrix?
A) $Z_{11} = Z_{22}$ and $Z_{12} = Z_{21}$
B) $Z_{11}Z_{22} - Z_{12}Z_{21} = 0$
C) $Z_{11} = Z_{22}$ and $Z_{12} = Z_{21} = 0$
D) $Z_{12} = Z_{21}$ and $Z_{11} = Z_{22}$ only if the network is passive.
Correct Answer: A) $Z_{11} = Z_{22}$ and $Z_{12} = Z_{21}$
Explanation: Reciprocity in a two-port network requires $Z_{12} = Z_{21}$. Symmetry requires
that the input and output ports are indistinguishable, implying $Z_{11} = Z_{22}$. Option B
,represents the condition for a singular matrix, which is not a requirement for symmetry or
reciprocity. Option C incorrectly assumes the transfer impedances must be zero.
Question 3: In an RLC series circuit driven by a sinusoidal voltage source, the power factor is
observed to be 0.8 lagging. If the frequency of the source is doubled, what happens to the nature
of the power factor?
A) It becomes leading.
B) It remains lagging but the value increases.
C) It remains lagging but the value decreases.
D) It may become leading or remain lagging depending on the initial $Q$-factor.
Correct Answer: A) It becomes leading.
Explanation: A lagging power factor implies the inductive reactance $X_L = \omega L$
dominates the capacitive reactance $X_C = \frac{1}{\omega C}$. When frequency $\omega$
doubles, $X_L$ increases by a factor of 4 (relative to its initial state vs $X_C$). Wait—
recalculating: $X_L' = 2\omega L$ and $X_C' = \frac{1}{2\omega C} = \frac{X_C}{4}$. Since
$X_L$ was already greater than $X_C$, doubling the frequency makes $X_L$ even larger
relative to $X_C$, reinforcing the inductive (lagging) nature. Correction: If the circuit was
initially near resonance, doubling frequency pushes it into the inductive region. The prompt
implies a shift. If $X_L > X_C$, increasing frequency increases $X_L$ faster than it decreases
$X_C$, keeping it lagging.
Question 4: Consider a Tellegen’s Theorem application in a circuit with $n$ branches. Which of
the following is a fundamental prerequisite for the summation of branch power to equal zero?
A) The circuit must be purely resistive.
B) The currents must satisfy KCL and the voltages must satisfy KVL simultaneously.
C) The circuit must be in a steady-state condition.
D) The network must be planar.
Correct Answer: B) The currents must satisfy KCL and the voltages must satisfy KVL
simultaneously.
Explanation: Tellegen’s Theorem is a topological property of any lumped circuit. It states that
for any set of branch voltages $v_k$ and currents $i_k$ that satisfy KVL and KCL respectively,
$\sum v_k i_k = 0$. It does not require linearity, time-invariance, or passivity. Options A, C, and
D are restrictive and unnecessary.
,Question 5: A balanced three-phase delta-connected load is supplied by a balanced star-
connected source. If one of the delta-load impedances is disconnected (open-circuited), what is
the impact on the line currents?
A) All line currents become zero.
B) Only two line currents remain equal; the third changes significantly.
C) The line currents become unbalanced and change in magnitude and phase.
D) The line currents remain unchanged due to phase symmetry.
Correct Answer: C) The line currents become unbalanced and change in magnitude and
phase.
Explanation: In a delta connection, each load impedance is connected across a line voltage.
Removing one branch breaks the symmetry of the phase currents. Since line currents are the
vector difference of the phase currents, a change in one phase current inevitably propagates to
the line currents, resulting in an unbalanced state.
Question 6: In a MOSFET-based amplifier circuit, what is the significance of the Early Effect on
the output resistance $r_o$?
A) It decreases $r_o$ as the channel length modulation increases.
B) It increases $r_o$ because the depletion region widens.
C) It has no effect on $r_o$ in an ideal model.
D) It makes $r_o$ frequency-dependent.
Correct Answer: A) It decreases $r_o$ as the channel length modulation increases.
Explanation: The Early Effect (or channel length modulation in MOSFETs) implies that the
drain current $i_D$ is not perfectly independent of $v_{DS}$. As $v_{DS}$ increases, the
effective channel length decreases, leading to an increase in $i_D$. The output resistance $r_o
= (\frac{\partial i_D}{\partial v_{DS}})^{-1}$. A finite slope in the $i_D$-$v_{DS}$ curve
results in a finite $r_o$. Greater channel length modulation reduces $r_o$.
Question 7: A second-order low-pass filter has a transfer function $H(s) =
\frac{\omega_n^2}{s^2 + 2\zeta\omega_n s + \omega_n^2}$. If the damping ratio $\zeta > 1$,
the circuit is classified as:
A) Underdamped
B) Critically damped
, C) Overdamped
D) Undamped
Correct Answer: C) Overdamped
Explanation: For a second-order system, the roots of the characteristic equation $s^2 +
2\zeta\omega_n s + \omega_n^2 = 0$ determine the response. If $\zeta > 1$, the roots are real
and distinct, leading to an overdamped response. $\zeta < 1$ is underdamped, $\zeta = 1$ is
critically damped, and $\zeta = 0$ is undamped (oscillatory).
Question 8: In an ideal transformer, the dot convention indicates the polarity of the induced
voltage. If current enters the dotted terminal of the primary, the induced voltage in the
secondary:
A) Is negative at the dotted terminal.
B) Is positive at the dotted terminal.
C) Remains zero.
D) Is 180 degrees out of phase with the primary voltage.
Correct Answer: B) Is positive at the dotted terminal.
Explanation: The dot convention states that if current enters the dotted terminal of one coil, the
voltage induced in the other coil will be positive at its dotted terminal. This is a fundamental rule
for magnetic coupling analysis in circuit theory.
Question 9: What is the primary advantage of using a Wien Bridge oscillator over a Phase Shift
oscillator in high-frequency applications?
A) Higher stability and easier frequency tuning.
B) Lower component count.
C) Ability to generate higher amplitude signals.
D) Superior harmonic distortion profile.
Correct Answer: A) Higher stability and easier frequency tuning.
Explanation: The Wien Bridge oscillator is highly valued for its frequency stability and the fact
that its frequency can be tuned using a single-gang variable capacitor or resistor. Phase shift
oscillators are generally more difficult to tune and suffer from greater frequency instability due
to the reliance on multiple RC sections.
Master Circuit Analysis Practice Questions &
Detailed Explanations
Subject: Electrical Engineering - Advanced Circuit Analysis
Question 1: In a non-linear resistive network, the dynamic resistance $r_d$ is defined as the
slope of the voltage-current characteristic curve. If a device exhibits a characteristic defined by
$i = I_0(e^{v/V_T} - 1)$, determine the expression for dynamic conductance $g_d$ in terms of
current $i$.
A) $g_d = \frac{i}{V_T}$
B) $g_d = \frac{i + I_0}{V_T}$
C) $g_d = \frac{V_T}{i}$
D) $g_d = \frac{I_0}{V_T}e^{v/V_T}$
Correct Answer: B) $g_d = \frac{i + I_0}{V_T}$
Explanation: The dynamic conductance is $g_d = \frac{di}{dv}$. Given $i = I_0(e^{v/V_T} -
1)$, differentiating with respect to $v$ yields $\frac{di}{dv} = \frac{I_0}{V_T}e^{v/V_T}$. From
the original equation, $i + I_0 = I_0e^{v/V_T}$. Substituting this into the derivative expression,
we obtain $g_d = \frac{i + I_0}{V_T}$. Option A is incorrect as it neglects the saturation
current $I_0$.
Question 2: A two-port network is characterized by its $Z$-parameters. If the network is
reciprocal and symmetric, which of the following conditions must hold true for the $Z$-matrix?
A) $Z_{11} = Z_{22}$ and $Z_{12} = Z_{21}$
B) $Z_{11}Z_{22} - Z_{12}Z_{21} = 0$
C) $Z_{11} = Z_{22}$ and $Z_{12} = Z_{21} = 0$
D) $Z_{12} = Z_{21}$ and $Z_{11} = Z_{22}$ only if the network is passive.
Correct Answer: A) $Z_{11} = Z_{22}$ and $Z_{12} = Z_{21}$
Explanation: Reciprocity in a two-port network requires $Z_{12} = Z_{21}$. Symmetry requires
that the input and output ports are indistinguishable, implying $Z_{11} = Z_{22}$. Option B
,represents the condition for a singular matrix, which is not a requirement for symmetry or
reciprocity. Option C incorrectly assumes the transfer impedances must be zero.
Question 3: In an RLC series circuit driven by a sinusoidal voltage source, the power factor is
observed to be 0.8 lagging. If the frequency of the source is doubled, what happens to the nature
of the power factor?
A) It becomes leading.
B) It remains lagging but the value increases.
C) It remains lagging but the value decreases.
D) It may become leading or remain lagging depending on the initial $Q$-factor.
Correct Answer: A) It becomes leading.
Explanation: A lagging power factor implies the inductive reactance $X_L = \omega L$
dominates the capacitive reactance $X_C = \frac{1}{\omega C}$. When frequency $\omega$
doubles, $X_L$ increases by a factor of 4 (relative to its initial state vs $X_C$). Wait—
recalculating: $X_L' = 2\omega L$ and $X_C' = \frac{1}{2\omega C} = \frac{X_C}{4}$. Since
$X_L$ was already greater than $X_C$, doubling the frequency makes $X_L$ even larger
relative to $X_C$, reinforcing the inductive (lagging) nature. Correction: If the circuit was
initially near resonance, doubling frequency pushes it into the inductive region. The prompt
implies a shift. If $X_L > X_C$, increasing frequency increases $X_L$ faster than it decreases
$X_C$, keeping it lagging.
Question 4: Consider a Tellegen’s Theorem application in a circuit with $n$ branches. Which of
the following is a fundamental prerequisite for the summation of branch power to equal zero?
A) The circuit must be purely resistive.
B) The currents must satisfy KCL and the voltages must satisfy KVL simultaneously.
C) The circuit must be in a steady-state condition.
D) The network must be planar.
Correct Answer: B) The currents must satisfy KCL and the voltages must satisfy KVL
simultaneously.
Explanation: Tellegen’s Theorem is a topological property of any lumped circuit. It states that
for any set of branch voltages $v_k$ and currents $i_k$ that satisfy KVL and KCL respectively,
$\sum v_k i_k = 0$. It does not require linearity, time-invariance, or passivity. Options A, C, and
D are restrictive and unnecessary.
,Question 5: A balanced three-phase delta-connected load is supplied by a balanced star-
connected source. If one of the delta-load impedances is disconnected (open-circuited), what is
the impact on the line currents?
A) All line currents become zero.
B) Only two line currents remain equal; the third changes significantly.
C) The line currents become unbalanced and change in magnitude and phase.
D) The line currents remain unchanged due to phase symmetry.
Correct Answer: C) The line currents become unbalanced and change in magnitude and
phase.
Explanation: In a delta connection, each load impedance is connected across a line voltage.
Removing one branch breaks the symmetry of the phase currents. Since line currents are the
vector difference of the phase currents, a change in one phase current inevitably propagates to
the line currents, resulting in an unbalanced state.
Question 6: In a MOSFET-based amplifier circuit, what is the significance of the Early Effect on
the output resistance $r_o$?
A) It decreases $r_o$ as the channel length modulation increases.
B) It increases $r_o$ because the depletion region widens.
C) It has no effect on $r_o$ in an ideal model.
D) It makes $r_o$ frequency-dependent.
Correct Answer: A) It decreases $r_o$ as the channel length modulation increases.
Explanation: The Early Effect (or channel length modulation in MOSFETs) implies that the
drain current $i_D$ is not perfectly independent of $v_{DS}$. As $v_{DS}$ increases, the
effective channel length decreases, leading to an increase in $i_D$. The output resistance $r_o
= (\frac{\partial i_D}{\partial v_{DS}})^{-1}$. A finite slope in the $i_D$-$v_{DS}$ curve
results in a finite $r_o$. Greater channel length modulation reduces $r_o$.
Question 7: A second-order low-pass filter has a transfer function $H(s) =
\frac{\omega_n^2}{s^2 + 2\zeta\omega_n s + \omega_n^2}$. If the damping ratio $\zeta > 1$,
the circuit is classified as:
A) Underdamped
B) Critically damped
, C) Overdamped
D) Undamped
Correct Answer: C) Overdamped
Explanation: For a second-order system, the roots of the characteristic equation $s^2 +
2\zeta\omega_n s + \omega_n^2 = 0$ determine the response. If $\zeta > 1$, the roots are real
and distinct, leading to an overdamped response. $\zeta < 1$ is underdamped, $\zeta = 1$ is
critically damped, and $\zeta = 0$ is undamped (oscillatory).
Question 8: In an ideal transformer, the dot convention indicates the polarity of the induced
voltage. If current enters the dotted terminal of the primary, the induced voltage in the
secondary:
A) Is negative at the dotted terminal.
B) Is positive at the dotted terminal.
C) Remains zero.
D) Is 180 degrees out of phase with the primary voltage.
Correct Answer: B) Is positive at the dotted terminal.
Explanation: The dot convention states that if current enters the dotted terminal of one coil, the
voltage induced in the other coil will be positive at its dotted terminal. This is a fundamental rule
for magnetic coupling analysis in circuit theory.
Question 9: What is the primary advantage of using a Wien Bridge oscillator over a Phase Shift
oscillator in high-frequency applications?
A) Higher stability and easier frequency tuning.
B) Lower component count.
C) Ability to generate higher amplitude signals.
D) Superior harmonic distortion profile.
Correct Answer: A) Higher stability and easier frequency tuning.
Explanation: The Wien Bridge oscillator is highly valued for its frequency stability and the fact
that its frequency can be tuned using a single-gang variable capacitor or resistor. Phase shift
oscillators are generally more difficult to tune and suffer from greater frequency instability due
to the reliance on multiple RC sections.
