Q.1 Which of the following represents the natural response of a first‑order RC circuit when the input voltage is suddenly removed?
Vc(t) = V0 e^(-t/RC)
Vc(t) = V0 e^(t/RC)
Vc(t) = V0 (1 - e^(-t/RC))
Vc(t) = V0 cos(t/RC)
Explanation - When the source is removed the capacitor discharges through the resistor with a time constant τ = RC, giving the exponential decay Vc(t) = V0 e^(-t/τ).
Correct answer is: Vc(t) = V0 e^(-t/RC)
Q.2 What is the unit of the time constant τ in a first‑order RL circuit?
Ohms
Henrys
Seconds
Volts
Explanation - The time constant τ = L/R has units of henrys divided by ohms, which simplifies to seconds.
Correct answer is: Seconds
Q.3 In an RLC series circuit driven by a step voltage, which term corresponds to the undamped natural frequency ω0?
ω0 = 1/√(LC)
ω0 = R/√(LC)
ω0 = √(L/C)
ω0 = R/L
Explanation - For a lossless series RLC, the natural frequency is ω0 = 1/√(LC). The resistance only introduces damping.
Correct answer is: ω0 = 1/√(LC)
Q.4 Which equation correctly relates the Laplace transform of a unit step function u(t) to its s-domain representation?
U(s) = 1/s
U(s) = s
U(s) = 1/(s+1)
U(s) = 0
Explanation - The Laplace transform of u(t) is 1/s, assuming zero initial conditions.
Correct answer is: U(s) = 1/s
Q.5 For a critically damped second‑order system, what is the relation between damping ratio ζ and natural frequency ω0?
ζ = 1
ζ = 0
ζ = 0.5
ζ = √2
Explanation - Critical damping occurs when the damping ratio ζ equals 1; the system returns to equilibrium without oscillation.
Correct answer is: ζ = 1
Q.6 Which of the following is the impulse response h(t) of an ideal differentiator circuit?
h(t) = δ(t)
h(t) = u(t)
h(t) = dt/dt
h(t) = 1
Explanation - An ideal differentiator has h(t) = δ(t) because its output is the derivative of the input, represented by the Dirac delta in the time domain.
Correct answer is: h(t) = δ(t)
Q.7 In a first‑order RC low‑pass filter, the -3 dB cutoff frequency fc is given by which expression?
fc = 1/(2πRC)
fc = 2πRC
fc = RC/(2π)
fc = 1/(RC)
Explanation - The -3 dB point occurs when the magnitude falls to 1/√2 of the passband, giving fc = 1/(2πRC).
Correct answer is: fc = 1/(2πRC)
Q.8 During the transient response of a series RLC circuit, the capacitor voltage peaks at a time tmax given by which formula?
tmax = π/(ω0) * sqrt(1 - ζ^2)
tmax = 1/(ω0 ζ)
tmax = ω0/ζ
tmax = ζ/ω0
Explanation - The time of the first peak in an underdamped second‑order system is tmax = (π/ωd) where ωd = ω0√(1-ζ^2).
Correct answer is: tmax = π/(ω0) * sqrt(1 - ζ^2)
Q.9 Which method is commonly used to convert a differential equation of a linear time‑invariant circuit into the s‑domain?
Laplace Transform
Fourier Transform
Z‑Transform
Wavelet Transform
Explanation - The Laplace Transform turns differential equations into algebraic equations, simplifying the analysis of LTI circuits.
Correct answer is: Laplace Transform
Q.10 If an RLC series circuit has R=10 Ω, L=2 H and C=0.5 mF, what is its damping ratio ζ?
0.35
0.5
1
2
Explanation - Compute ω0 = 1/√(LC) = 1/√(2*0.0005)=1/√0.001=31.62 rad/s. Then ζ = R/(2√(L/C)) = 10/(2√(2/0.0005)) ≈ 0.35.
Correct answer is: 0.35
Q.11 Which of the following best describes the short‑circuit current of an RL circuit when a step voltage is applied?
It rises instantly to the maximum value.
It rises exponentially with time constant τ = L/R.
It oscillates indefinitely.
It decays exponentially.
Explanation - The current in an RL circuit starts at zero and approaches the steady‑state value exponentially with τ = L/R.
Correct answer is: It rises exponentially with time constant τ = L/R.
Q.12 In transient analysis, the term 'steady‑state' refers to:
The condition as t → 0+.
The condition as t → ∞.
The maximum transient value.
The frequency response.
Explanation - Steady‑state is the long‑term behavior after all transients have decayed (t → ∞).
Correct answer is: The condition as t → ∞.
Q.13 For an underdamped RLC series circuit, the response of the capacitor voltage includes which of the following terms?
A single exponential decay
A sinusoid multiplied by an exponential decay
Only a sinusoid
Only a constant
Explanation - The underdamped response is a damped sinusoid: Vc(t) = V0 e^(-ζω0 t) sin(ωd t + φ).
Correct answer is: A sinusoid multiplied by an exponential decay
Q.14 When an RL circuit is switched into a DC source, which component stores energy during the transient?
Resistor
Inductor
Capacitor
Voltage source
Explanation - The inductor stores magnetic energy (½ L I²) during the transient before reaching steady state.
Correct answer is: Inductor
Q.15 What is the expression for the energy stored in a capacitor of capacitance C at voltage Vc?
½ C Vc²
½ L I²
C Vc
Vc / C
Explanation - The electrostatic energy in a capacitor is U = ½ C V².
Correct answer is: ½ C Vc²
Q.16 Which of the following best describes the step response of an overdamped second‑order system?
A single exponential decay with no oscillations.
An oscillatory response with exponential decay.
A constant offset with no decay.
A sinusoid of constant amplitude.
Explanation - Overdamped systems have two real negative poles; the response is a sum of two exponential terms with no oscillation.
Correct answer is: A single exponential decay with no oscillations.
Q.17 The transfer function H(s) of a first‑order low‑pass filter is given by H(s) = 1/(τs + 1). What is the magnitude response |H(jω)| at ω = 0?
1
0
∞
τ
Explanation - At zero frequency, H(0) = 1/1 = 1, indicating unity gain in the passband.
Correct answer is: 1
Q.18 During the transient response of a capacitor in an RC circuit, the voltage Vc(t) equals Vmax when which condition is true?
t = τ
t = 0
t = 5τ
t = ∞
Explanation - By the rule of thumb, after 5 time constants the voltage has reached 99.3% of its final value.
Correct answer is: t = 5τ
Q.19 In the Laplace domain, which of the following represents the transform of a capacitor's voltage when its initial voltage is V0?
Vc(s) = V0/s + I(s)/(Cs)
Vc(s) = V0 s + I(s)/C
Vc(s) = V0/(s + 1/RC)
Vc(s) = I(s)/Cs
Explanation - The transform includes the initial condition term V0/s plus the term due to the Laplace of the current.
Correct answer is: Vc(s) = V0/s + I(s)/(Cs)
Q.20 What is the definition of the damping coefficient β in a second‑order circuit?
β = R/(2L)
β = L/(2R)
β = 1/(2RC)
β = R/(LC)
Explanation - In the standard form d²x/dt² + 2β dx/dt + ω0² x = 0, β is R/(2L) for a series RLC.
Correct answer is: β = R/(2L)
Q.21 Which of the following statements about the impedance of an inductor is FALSE?
Impedance increases with frequency.
Impedance is purely real.
Impedance magnitude is ωL.
Impedance is jωL.
Explanation - Inductor impedance is purely imaginary (jωL); it is not real.
Correct answer is: Impedance is purely real.
Q.22 The natural response of an RLC circuit is also known as:
Forced response
Transients
Steady‑state
Resonant response
Explanation - Natural response is the system’s reaction to initial conditions without external excitation; it is the transient part.
Correct answer is: Transients
Q.23 For an underdamped second‑order system, which of these is the expression for the damping ratio ζ in terms of the poles p1 and p2?
ζ = (p1 + p2)/2
ζ = (p1 - p2)/2
ζ = -(Re(p1) + Re(p2))/(2ω0)
ζ = √(p1 p2)/ω0
Explanation - The damping ratio is defined by the negative real parts of the poles divided by twice the natural frequency.
Correct answer is: ζ = -(Re(p1) + Re(p2))/(2ω0)
Q.24 Which circuit element is responsible for storing energy in a magnetic field during a transient?
Capacitor
Resistor
Inductor
Diode
Explanation - An inductor stores energy magnetically in its magnetic field.
Correct answer is: Inductor
Q.25 If the time constant τ of an RC circuit is 4 ms, how many seconds will it take for the capacitor voltage to reach 99% of its final value?
0.02 s
0.08 s
0.004 s
0.0004 s
Explanation - 5 time constants equal 5×4 ms = 20 ms = 0.02 s for 99% completion.
Correct answer is: 0.02 s
Q.26 During the transient analysis of an RC network, the Laplace transform of the output voltage Vout(s) when the input Vin(s) is a step of magnitude V0 is given by:
Vout(s) = (V0/s) * (1/(1+RCs))
Vout(s) = (V0/s) * (RCs + 1)
Vout(s) = (V0/s) * (RCs)
Vout(s) = (V0/s) * (sRC)
Explanation - The transfer function of a first‑order low‑pass filter is 1/(1+RCs), multiplied by the step source V0/s.
Correct answer is: Vout(s) = (V0/s) * (1/(1+RCs))
Q.27 In a series RLC circuit with R=0, which of the following best describes the natural response?
A single exponential decay
A sinusoid of constant amplitude
A step response
A DC offset
Explanation - With no resistance, the system is lossless and will oscillate indefinitely at ω0.
Correct answer is: A sinusoid of constant amplitude
Q.28 What is the initial current through an inductor when a voltage step V0 is applied across an RL series circuit at t = 0+?
0 A
V0/R
∞
V0/L
Explanation - An inductor resists instantaneous change in current; the initial current is zero.
Correct answer is: 0 A
Q.29 Which of the following statements best describes the concept of a 'transient' in electrical circuits?
The steady‑state response to a continuous input.
The response caused by a sudden change in initial conditions.
The response to a periodic input.
The DC offset of a signal.
Explanation - Transients arise from changes in initial conditions or sudden changes in input; they decay over time.
Correct answer is: The response caused by a sudden change in initial conditions.
Q.30 In an RC circuit, if the capacitor is initially charged to V0 and the resistor is suddenly removed, what happens to the capacitor voltage?
It remains at V0 indefinitely.
It drops to zero instantly.
It increases to twice V0.
It oscillates.
Explanation - With no resistor, there is no path for current; the capacitor stays charged at V0.
Correct answer is: It remains at V0 indefinitely.
Q.31 Which of the following best describes the magnitude of a transfer function H(s) at very high frequencies for a first‑order low‑pass filter?
0
1
∞
1/RC
Explanation - High frequencies are heavily attenuated in a low‑pass filter, giving magnitude approaching zero.
Correct answer is: 0
Q.32 The step response of an overdamped second‑order system can be written as a sum of exponentials. What determines the relative amplitudes of these exponentials?
Initial conditions and system poles
The input voltage magnitude only
The resistor value only
The natural frequency only
Explanation - The coefficients depend on the initial state and the location of the two real poles.
Correct answer is: Initial conditions and system poles
Q.33 Which of the following is true about the energy stored in an inductor during the transient period of an RL circuit?
It decreases linearly with time.
It increases exponentially to a maximum and then decreases.
It remains constant.
It is zero until steady state.
Explanation - Energy (½ L I²) rises as current builds, reaching a maximum when current stabilizes at V/R, then remains constant.
Correct answer is: It increases exponentially to a maximum and then decreases.
Q.34 When analyzing a circuit in the time domain, why is the Laplace transform often preferred over differential equations?
It eliminates the need for initial conditions.
It converts differential equations into algebraic equations.
It gives the Fourier transform of the signal.
It simplifies to a DC equivalent circuit.
Explanation - The Laplace transform linearizes circuit equations, making them easier to solve.
Correct answer is: It converts differential equations into algebraic equations.
Q.35 In a step response analysis, which of the following best describes the 'rise time' of a first‑order RC circuit?
Time taken for the voltage to reach 50% of final value.
Time taken to reach 10% to 90% of final value.
Time taken to reach 90% to 99% of final value.
Time taken to reach 99% to 100% of final value.
Explanation - Rise time is conventionally defined as the interval between 10% and 90% of the final value.
Correct answer is: Time taken to reach 10% to 90% of final value.
Q.36 Which of the following best describes a 'critical step' in a second‑order system?
A step that causes the system to oscillate with maximum amplitude.
A step that causes the system to return to equilibrium without oscillation.
A step that produces a zero response.
A step that changes the system’s damping ratio.
Explanation - A critically damped response (ζ=1) returns to steady state as quickly as possible without overshoot.
Correct answer is: A step that causes the system to return to equilibrium without oscillation.
Q.37 The natural response of a circuit can be derived by solving which mathematical equation?
Homogeneous differential equation
Non‑homogeneous differential equation
Algebraic equation
Integral equation
Explanation - The natural response comes from the homogeneous part of the differential equation (zero input).
Correct answer is: Homogeneous differential equation
Q.38 In the context of transient analysis, what does the 'time constant' τ represent in an RC circuit?
The time for the capacitor voltage to reach 50% of its final value.
The time for the capacitor voltage to reach 63.2% of its final value.
The time for the resistor voltage to reach 63.2% of its final value.
The time for the current to decay to zero.
Explanation - τ = RC; the capacitor voltage reaches (1‑e⁻¹) ≈ 63.2% of its final value after one time constant.
Correct answer is: The time for the capacitor voltage to reach 63.2% of its final value.
Q.39 Which of the following best describes the concept of 'steady‑state' in the frequency domain?
The system output after all transients have decayed.
The maximum output amplitude for any input.
The output when the input is zero.
The output at t = 0.
Explanation - Steady‑state refers to the long‑term response when all transient effects have vanished.
Correct answer is: The system output after all transients have decayed.
Q.40 Which of these is a typical application of transient analysis in power electronics?
Designing steady‑state filters
Analyzing switching transients in DC‑DC converters
Calculating DC power consumption
Optimizing frequency response of amplifiers
Explanation - Transients arise when switches change state; analysis is essential for converter design.
Correct answer is: Analyzing switching transients in DC‑DC converters
Q.41 In a series RLC circuit, which parameter determines the period of oscillation in the underdamped case?
Time constant τ = L/R
Natural frequency ω0 = 1/√(LC)
Damping ratio ζ = R/(2L)
Impedance magnitude Z = √(R² + (ωL - 1/ωC)²)
Explanation - The damped natural frequency ωd depends on ω0 and ζ, but ω0 sets the fundamental oscillation period.
Correct answer is: Natural frequency ω0 = 1/√(LC)
Q.42 What is the Laplace transform of a resistor's voltage drop V_R(t) = I(t) R when I(t) has initial value I0?
V_R(s) = R I0 + R I(s)
V_R(s) = R I0/s + R I(s)
V_R(s) = R I0 s + R I(s)
V_R(s) = R I(s)/s
Explanation - The Laplace of I(t) includes the initial current term I0 and the Laplace of the time‑varying part.
Correct answer is: V_R(s) = R I0 + R I(s)
Q.43 Which of the following best explains why an inductor’s voltage leads the current by 90 degrees?
Because of its resistive nature.
Because of its ability to store magnetic energy.
Because of its capacitive effect.
Because it provides a constant voltage.
Explanation - Inductor voltage V = L di/dt, so a change in current (di/dt) occurs ahead of the voltage, giving a 90° lead.
Correct answer is: Because of its ability to store magnetic energy.
Q.44 When solving the transient response of a parallel RLC circuit, the differential equation is of what order?
First order
Second order
Third order
Fourth order
Explanation - A parallel RLC has two energy storage elements (L and C), leading to a second‑order differential equation.
Correct answer is: Second order
Q.45 Which of the following best describes the effect of increasing resistance in a series RLC circuit on the transient response?
It increases the overshoot.
It decreases the damping ratio.
It causes the circuit to become underdamped.
It increases the damping ratio.
Explanation - Higher R leads to larger ζ, making the response more heavily damped.
Correct answer is: It increases the damping ratio.
Q.46 The magnitude of the transfer function H(jω) of a first‑order high‑pass filter is given by:
|H(jω)| = ωRC / √(1 + (ωRC)²)
|H(jω)| = 1 / √(1 + (ωRC)²)
|H(jω)| = √(1 + (ωRC)²)
|H(jω)| = 1 / (ωRC)
Explanation - The high‑pass magnitude response rises with frequency, reaching unity as ω → ∞.
Correct answer is: |H(jω)| = ωRC / √(1 + (ωRC)²)
Q.47 Which of these best represents the unit of the Laplace variable s?
Seconds
Radians per second
Henrys
Seconds⁻¹
Explanation - The Laplace variable s has units of reciprocal time (s⁻¹).
Correct answer is: Seconds⁻¹
Q.48 During transient analysis, which of the following is NOT a boundary condition needed to solve a second‑order differential equation?
Initial voltage across the capacitor
Initial current through the inductor
Final steady‑state value
Input source characteristics
Explanation - Initial conditions are required; the final value is determined by the solution, not a boundary condition.
Correct answer is: Final steady‑state value
Q.49 A circuit’s step response reaches 99% of the final value after how many time constants τ in a first‑order system?
1 τ
2 τ
3 τ
5 τ
Explanation - At 5τ the response is approximately 99.3% of its final value.
Correct answer is: 5 τ
Q.50 In a series RLC circuit, the natural resonant frequency ω0 is given by:
ω0 = √(L/C)
ω0 = 1/√(LC)
ω0 = R/(L C)
ω0 = √(C/L)
Explanation - The undamped natural frequency of a lossless series RLC is ω0 = 1/√(LC).
Correct answer is: ω0 = 1/√(LC)
Q.51 Which of these is an example of a natural response that decays to zero as t → ∞?
An exponential decay term e^(-t/τ)
A constant DC offset
A sinusoidal steady‑state signal
An impulse function δ(t)
Explanation - Exponential decays vanish over time; constants and sinusoids persist.
Correct answer is: An exponential decay term e^(-t/τ)
Q.52 In a step response of an overdamped RLC circuit, the time constants τ1 and τ2 are related to which of the following parameters?
Natural frequency ω0 and damping ratio ζ
Resistance R only
Capacitance C only
Inductor L only
Explanation - The two real poles are functions of ω0 and ζ, giving two distinct time constants.
Correct answer is: Natural frequency ω0 and damping ratio ζ
Q.53 Which of the following describes the phase shift of a first‑order RC low‑pass filter at the cutoff frequency?
0°
45°
90°
-45°
Explanation - At ωc = 1/RC, the phase shift is -45° relative to the input.
Correct answer is: -45°
Q.54 If a step input is applied to a series RLC circuit, the voltage across the inductor initially is:
Zero
The full step voltage
Half the step voltage
The same as the capacitor voltage
Explanation - An inductor resists sudden changes, so its initial voltage is zero when the step is applied.
Correct answer is: Zero
Q.55 The transient response of an LRC series circuit can be represented as a sum of two exponentials. What condition must be true for these exponentials to have the same time constant?
R = 0
L = C
R is very large
ω0 = 0
Explanation - Only when R=0 do the poles coalesce into a repeated real pole, giving the same time constant.
Correct answer is: R = 0
Q.56 During the transient analysis of an RC circuit, the term Vc(t) = V0(1 - e^(-t/RC)) is derived from solving:
a first‑order differential equation
a second‑order differential equation
an algebraic equation
a partial differential equation
Explanation - The capacitor voltage obeys dVc/dt + (1/RC)Vc = V0/RC, a first‑order ODE.
Correct answer is: a first‑order differential equation
Q.57 In Laplace analysis, the term sI(s) often appears. What physical quantity does it represent?
Initial current value
Current derivative
Capacitance effect
Resistor voltage drop
Explanation - sI(s) includes the initial current I(0+) as part of the transform of a derivative.
Correct answer is: Initial current value
Q.58 Which of these best describes an underdamped system’s transient response?
A monotonic decay without oscillation.
A decaying sinusoid that overshoots.
A constant value with no decay.
An exponential rise to a fixed value.
Explanation - Underdamped response includes oscillations that decay over time.
Correct answer is: A decaying sinusoid that overshoots.
Q.59 A capacitor discharges through a resistor of value R. If the initial voltage on the capacitor is 12 V, the voltage after 3τ will be:
12 V
4.5 V
0.5 V
0 V
Explanation - Vc(3τ) = 12 e^(-3) ≈ 0.5 V.
Correct answer is: 0.5 V
Q.60 In a parallel RLC circuit, the total impedance Z(s) at s = jω is given by:
1/(1/R + sC + 1/(sL))
R + sL + 1/(sC)
R + 1/(sL) + sC
R + sL - sC
Explanation - Parallel impedances combine reciprocally: 1/Z = 1/R + sC + 1/(sL).
Correct answer is: 1/(1/R + sC + 1/(sL))
Q.61 The time constant τ of a first‑order RC low‑pass filter determines the slope of the logarithmic magnitude plot at which frequency?
ω = 0
ω = ωc
ω = ∞
ω = 2ωc
Explanation - The slope at the cutoff frequency is –20 dB/decade, determined by τ.
Correct answer is: ω = ωc
Q.62 Which of the following is true for a purely resistive circuit when a step voltage is applied?
The current rises instantly to its steady‑state value.
The voltage across the resistor oscillates.
The current decays to zero.
There is no transient.
Explanation - In a pure resistor, current follows voltage instantly; no energy storage, no transient.
Correct answer is: The current rises instantly to its steady‑state value.
Q.63 The impulse response of an ideal integrator circuit is:
δ(t)
u(t)
t
1
Explanation - Integrating a Dirac delta gives a unit step function.
Correct answer is: u(t)
Q.64 When converting a differential equation to the s‑domain, which initial condition is typically represented by the term k/s?
Initial voltage across a capacitor
Initial current through an inductor
Initial charge on a capacitor
Initial energy stored in an inductor
Explanation - The voltage term appears as k/s, where k is the initial voltage.
Correct answer is: Initial voltage across a capacitor
Q.65 Which of these statements about the Bode plot of a second‑order system is FALSE?
The magnitude plot has a corner at the natural frequency.
The phase shift goes from 0° to -180°.
The slope changes by +20 dB/dec at each pole.
The system's damping ratio affects the width of the peak.
Explanation - Each pole decreases the slope by -20 dB/dec, not increases.
Correct answer is: The slope changes by +20 dB/dec at each pole.
Q.66 A circuit has a step input of amplitude V0. If the transfer function H(s) = 1/(s + a), what is the time domain output v(t)?
V0 e^(-a t)
V0 (1 - e^(-a t))
V0 e^(a t)
V0 (1 + e^(-a t))
Explanation - Inverse Laplace: V0/s * 1/(s+a) = V0(1 - e^(-a t)).
Correct answer is: V0 (1 - e^(-a t))
Q.67 The unit of a time constant τ in seconds is also the unit of:
Frequency
Impedance
Phase
Gain
Explanation - Frequency is measured in Hz, which is cycles per second, the reciprocal of seconds.
Correct answer is: Frequency
Q.68 In a first‑order RL circuit, what is the expression for the current I(t) after a step voltage V0 is applied?
I(t) = (V0/R)(1 - e^(-R t/L))
I(t) = (V0/L)(1 - e^(-L t/R))
I(t) = V0 e^(-t/τ)
I(t) = V0 e^(t/τ)
Explanation - Current builds exponentially to V0/R with time constant τ = L/R.
Correct answer is: I(t) = (V0/R)(1 - e^(-R t/L))
Q.69 Which of the following is a characteristic of a critically damped RLC circuit?
The response has maximum overshoot.
The system returns to equilibrium as quickly as possible without oscillation.
The system oscillates indefinitely.
The response is a single exponential decay.
Explanation - Critical damping (ζ=1) gives the fastest return to steady state without overshoot.
Correct answer is: The system returns to equilibrium as quickly as possible without oscillation.
Q.70 In transient analysis, which of the following best describes the effect of an ideal capacitor when a sudden DC voltage is applied?
The voltage across the capacitor instantly jumps to the source voltage.
The current through the capacitor is zero at all times.
The voltage across the capacitor remains at its initial value until it changes.
The current through the capacitor is infinite at t = 0.
Explanation - An ideal capacitor resists sudden changes in voltage; it holds its initial voltage.
Correct answer is: The voltage across the capacitor remains at its initial value until it changes.
Q.71 Which of the following equations gives the period T of oscillation in an ideal LC circuit?
T = 2π√(LC)
T = 1/(2π√(LC))
T = 2πL/C
T = √(L/C)
Explanation - The natural period of a lossless LC oscillator is T = 2π√(LC).
Correct answer is: T = 2π√(LC)
Q.72 Which of these represents a valid initial condition for a second‑order differential equation describing an RLC circuit?
Voltage across the capacitor at t=0
Derivative of voltage at t=∞
Current through the resistor at t=10 s
Frequency of the source at t=0
Explanation - Initial conditions are values at t=0; voltage and current are typical.
Correct answer is: Voltage across the capacitor at t=0
Q.73 For a step response of a first‑order RC network, the time constant τ can be expressed in terms of which parameters?
R and C only
L and C only
R and L only
R, L, and C
Explanation - τ = RC for an RC network.
Correct answer is: R and C only
Q.74 In transient analysis, the term 'impulse response' refers to the output when the input is:
A step function
A sine wave
A Dirac delta function
A constant voltage
Explanation - Impulse response h(t) is the system output to δ(t).
Correct answer is: A Dirac delta function
Q.75 Which of the following best explains why a capacitor’s voltage cannot change instantaneously?
Because its voltage is directly proportional to current.
Because it stores energy in a magnetic field.
Because its voltage depends on the integral of current.
Because it has zero resistance.
Explanation - Vc = (1/C)∫I dt; sudden current would require infinite change in voltage.
Correct answer is: Because its voltage depends on the integral of current.
Q.76 Which of these statements about the damping ratio ζ is FALSE?
ζ = R/(2L)
ζ < 1 indicates underdamping.
ζ > 1 indicates overdamping.
ζ = 0 indicates critical damping.
Explanation - ζ = 0 is lossless, leading to undamped oscillations; ζ = 1 is critical damping.
Correct answer is: ζ = 0 indicates critical damping.
Q.77 In a series RLC circuit driven by a sinusoidal source, the magnitude of the voltage across the inductor at resonance is:
Equal to the source voltage.
Infinite.
Zero.
Equal to R times the current.
Explanation - At resonance the inductive and capacitive reactances cancel, leaving only R, leading to infinite voltage theoretically.
Correct answer is: Infinite.
Q.78 Which of the following represents the natural response of a parallel RLC circuit when all external sources are removed?
A sum of exponential decays.
A constant DC value.
A sine wave with constant amplitude.
A step function.
Explanation - Parallel RLC has two energy storage elements leading to exponential decays governed by the poles.
Correct answer is: A sum of exponential decays.
Q.79 For a first‑order RC high‑pass filter, the cutoff frequency f_c is given by:
f_c = 1/(2πRC)
f_c = 2πRC
f_c = RC/(2π)
f_c = 1/(RC)
Explanation - High‑pass cutoff occurs at f_c = 1/(2πRC).
Correct answer is: f_c = 1/(2πRC)
Q.80 Which of the following is the correct expression for the time constant τ in a second‑order underdamped RLC circuit?
τ = 2L/R
τ = R/L
τ = L/(2R)
τ = 2R/L
Explanation - The damping coefficient β = R/(2L), so τ = 1/β = 2L/R.
Correct answer is: τ = 2L/R
Q.81 In transient analysis, the term 'zero‑order hold' refers to:
Keeping the input constant between samples.
An ideal transformer with no leakage.
A resistor with zero resistance.
A capacitor that holds zero voltage.
Explanation - Zero‑order hold holds the sampled input value constant until the next sample.
Correct answer is: Keeping the input constant between samples.
Q.82 Which of these best describes the natural frequency ω0 for an RLC series circuit when R is non‑zero?
ω0 = 1/√(LC) independent of R
ω0 = R/(2L)
ω0 = √(L/C)
ω0 = R/(LC)
Explanation - Natural frequency is determined by L and C only; R only introduces damping.
Correct answer is: ω0 = 1/√(LC) independent of R
Q.83 Which of the following is true for a step response of an overdamped system?
The response is oscillatory.
The response overshoots the final value.
The response consists of a single exponential term.
The response consists of the sum of two exponentials with different time constants.
Explanation - Overdamped response has two distinct real poles giving two exponentials.
Correct answer is: The response consists of the sum of two exponentials with different time constants.
Q.84 What is the unit of the Laplace variable s when solving transient problems?
Volts
Ohms
Seconds
Hz
Explanation - s has units of 1/second (Hz).
Correct answer is: Hz
Q.85 The transfer function H(s) of a second‑order low‑pass filter with ζ = 0.7 and ω0 = 10 rad/s is:
H(s) = 1/(s² + 14s + 100)
H(s) = 1/(s² + 0.7s + 100)
H(s) = 1/(s² + 14s + 200)
H(s) = 1/(s² + 7s + 100)
Explanation - General form H(s) = 1/(s² + 2ζω0 s + ω0²). For ζ=0.7, ω0=10 → 2ζω0=14, ω0²=100.
Correct answer is: H(s) = 1/(s² + 14s + 100)
Q.86 During transient analysis of a capacitor, the term 'charge Q(t)' satisfies which differential equation?
dQ/dt + (1/RC) Q = V(t)/R
d²Q/dt² + (1/RC) dQ/dt + Q = 0
dQ/dt + (1/RC) Q = 0
dQ/dt = V(t)/L
Explanation - Current I = dQ/dt; voltage across resistor V_R = I R, leading to the first‑order ODE.
Correct answer is: dQ/dt + (1/RC) Q = V(t)/R
Q.87 In a series RLC circuit, the quality factor Q is defined as:
Q = ω0 L / R
Q = R / (ω0 L)
Q = R / (ω0 C)
Q = ω0 C / R
Explanation - Quality factor Q = ω0 L / R = 1/(2ζ).
Correct answer is: Q = ω0 L / R
Q.88 Which of the following best describes the effect of a large time constant τ in an RC circuit on the step response?
It speeds up the rise time.
It slows down the rise time.
It increases the overshoot.
It has no effect on the response.
Explanation - A larger τ (RC) means slower exponential growth/decay.
Correct answer is: It slows down the rise time.
Q.89 In transient analysis, the 'zero‑frequency gain' of a system is:
The gain as s → ∞
The gain at the resonant frequency
The gain as s → 0
The maximum gain over all frequencies
Explanation - Zero‑frequency (DC) gain is the system output when the input is a constant.
Correct answer is: The gain as s → 0
Q.90 A step response of a second‑order system with ζ = 0.5 and ω0 = 20 rad/s will have:
A single exponential decay.
A damped sinusoid with 20% overshoot.
An undamped sinusoid.
An exponentially decaying sinusoid with no overshoot.
Explanation - ζ=0.5 indicates underdamping; the overshoot ≈ e^(-ζπ/√(1-ζ²)).
Correct answer is: A damped sinusoid with 20% overshoot.
Q.91 In the time domain, the convolution integral v_out(t) = ∫ h(τ) v_in(t-τ) dτ represents:
The frequency response of the system.
The impedance of the circuit.
The system's impulse response.
The system's step response.
Explanation - Convolution with the impulse response h(t) gives the output for any input.
Correct answer is: The system's impulse response.
Q.92 Which of the following is the correct expression for the damping coefficient β in a second‑order RLC circuit?
β = R/(2L)
β = L/(2R)
β = R/(2C)
β = C/(2R)
Explanation - β = R/(2L) appears in the standard form d²x/dt² + 2β dx/dt + ω0²x = 0.
Correct answer is: β = R/(2L)
Q.93 When applying a step voltage to an RL circuit, the current I(t) reaches 63.2% of its final value at:
t = τ/2
t = τ
t = 2τ
t = 5τ
Explanation - The time constant τ is defined by the 63.2% point for first‑order systems.
Correct answer is: t = τ
Q.94 The energy stored in an inductor L with current I is:
½ L I
½ C V²
½ L I²
L I
Explanation - Magnetic energy in an inductor is U = ½ L I².
Correct answer is: ½ L I²
Q.95 A capacitor of capacitance C discharges through a resistor R with initial voltage V0. The voltage across the capacitor after time t is:
V0 e^(t/RC)
V0 e^(-t/RC)
V0 (1 - e^(-t/RC))
V0 (1 + e^(-t/RC))
Explanation - The discharge follows Vc(t) = V0 e^(-t/τ) with τ = RC.
Correct answer is: V0 e^(-t/RC)
Q.96 In transient analysis, the term 'step input' refers to:
A constant source applied for a finite time.
A sudden change from zero to a constant value.
A sinusoidal source.
An impulse of zero width.
Explanation - A step input is a unit step function u(t).
Correct answer is: A sudden change from zero to a constant value.
Q.97 Which of the following best describes a 'transient' in the context of a capacitor in an RC circuit?
The steady‑state voltage across the capacitor.
The instantaneous change of voltage at t = 0.
The time‑varying voltage that decays to zero.
The DC bias voltage.
Explanation - Transient refers to the decaying exponential part of the response.
Correct answer is: The time‑varying voltage that decays to zero.
Q.98 Which of the following is the correct expression for the Laplace transform of a capacitor with initial voltage V0?
C(s) = V0/s + I(s)/s
C(s) = V0 s + I(s)/C
C(s) = V0/(s + 1/RC)
C(s) = I(s)/s
Explanation - The capacitor transform includes an initial voltage term V0/s and the current term I(s)/s.
Correct answer is: C(s) = V0/s + I(s)/s