First-Order Circuits: Interactive Learning Quizzes for Electrical Engineering Students

Question 1

How does the transient response of a first-order RL circuit differ when subjected to a step input versus a sinusoidal input?

Accepted Answer

Step input: exponential current rise to steady-state; Sinusoidal input: current oscillates at input frequency

Answer

Both inputs: exponential current rise

Answer

Identical transient response for both inputs

Question 2

In an LR circuit, how do inductance and resistance affect the current and voltage waveforms during a transient response?

Accepted Answer

Inductance resists current changes, slowing the rise and fall of current, while resistance limits the peak current.

Answer

Inductance speeds up the current rise and fall, while resistance has no impact on the current.

Answer

Resistance slows down the current, while inductance has no impact on the voltage.

Answer

Inductance and resistance have no effect on the transient response of an LR circuit.

Question 3

In a parallel RC circuit, what is the relationship between the voltage across the capacitor and the source voltage?

Accepted Answer

Equal to the source voltage

Answer

Proportional to the capacitor's resistance

Answer

Proportional to the capacitor's capacitance

Answer

Independent of the source voltage

Question 4

Which of the following is not a fundamental characteristic of first-order circuits?

Accepted Answer

Nonlinearity

Answer

Transient response

Answer

Steady-state response

Answer

Time invariance

Question 5

What is the transfer function of a parallel RC circuit?

Accepted Answer

Vout / Vin = 1 / (1 + RCs)

Answer

Vout / Vin = RCs

Answer

Vout / Vin = sRC

Answer

Vout / Vin = 1 / (sRC)

Question 6

What is the shape of the impulse response in first-order circuits?

Accepted Answer

Decaying exponential

Answer

Sinusoidal wave

Answer

Step function

Answer

Dirac delta function

Question 7

What type of frequency response is exhibited by a series RL circuit?

Accepted Answer

Low-pass

Answer

High-pass

Answer

Band-pass

Answer

Band-reject

Question 8

In a parallel RC circuit, what is the phase shift between the input and output signals?

Accepted Answer

90 degrees

Answer

0 degrees

Answer

180 degrees

Answer

270 degrees

Question 9

Which of the following circuits exhibits underdamped behavior?

Accepted Answer

Circuit with low resistance and high inductance

Answer

Circuit with high resistance and low inductance

Answer

Circuit with high resistance and high inductance

Answer

Circuit with low resistance and low inductance

Question 10

The energy stored in a capacitor is:

Accepted Answer

Proportional to the voltage squared

Answer

Proportional to the capacitance

Answer

Proportional to the voltage

Answer

Proportional to the capacitance squared

Question 11

Which of the following is NOT a characteristic of first-order circuits?

Accepted Answer

Can have multiple natural frequencies

Answer

Contain only one energy storage element

Answer

Response is exponential in nature

Answer

Time constant plays a crucial role

Question 12

The power dissipated in a resistor is given by:

Accepted Answer

I^2 * R

Answer

V^2 / R

Answer

V * I

Answer

V / I

Question 13

In transient analysis of first-order circuits, which method(s) can be employed?

Accepted Answer

Time-domain analysis

Accepted Answer

Laplace transform analysis

Answer

Frequency-domain analysis

Question 14

Which of the following characteristics does NOT apply to first-order RC circuits?

Accepted Answer

Supports resonance

Answer

Possesses a single energy storage element

Answer

Exhibits exponential voltage or current response

Answer

Demonstrates frequency-dependent behavior

Question 15

In a first-order LC circuit, which components exchange energy during oscillations?

Accepted Answer

Capacitor and inductor

Answer

Resistor and capacitor

Answer

Resistor and inductor

Answer

Capacitor and resistor

Question 16

Which factors influence the time constant of a first-order RL circuit?

Accepted Answer

Resistance and inductance

Answer

Capacitance and inductance

Answer

Resistance and capacitance

Answer

Frequency and voltage

Question 17

In a first-order LC circuit, what determines the resonant frequency?

Accepted Answer

Inductance and capacitance

Answer

Resistance and inductance

Answer

Capacitance and resistance

Answer

Voltage and frequency

Question 18

Which statement accurately describes first-order circuits?

Accepted Answer

They contain a single energy storage element.

Answer

They always exhibit oscillatory responses.

Answer

Their time constant remains constant.

Answer

They find no practical applications.

Question 19

In a first-order RL circuit, the current through the inductor initially matches the source current and gradually approaches a steady-state value. Which mathematical expression captures this behavior?

Accepted Answer

I(t) = I_0e^(-t/tau)

Answer

V(t) = V_0e^(-t/tau)

Answer

I(t) = I_0(1 - e^(-t/tau))

Answer

V(t) = V_0(1 - e^(-t/tau))

Question 20

Select the most common practical application of first-order RC circuits:

Accepted Answer

Timing circuits

Answer

Energy storage devices

Answer

Voltage regulators

Answer

Amplifiers

Question 21

After the switch has been closed for an extended period in a first-order RL circuit, the current through the inductor reaches:

Accepted Answer

Steady-state current level

Answer

Zero

Answer

Initial current level

Answer

Exponential decay

Question 22

The energy stored in a capacitor within a first-order RC circuit at a given time is:

Accepted Answer

1/2CV²

Answer

CV

Answer

1/2LI²

Answer

LI

Question 23

In a first-order LC circuit, the quality factor (Q) represents:

Accepted Answer

ω₀L/R

Answer

R/L

Answer

√(L/C)

Answer

ω₀C/R

Question 24

The voltage across a capacitor in a series RC circuit during charging is given by:

Accepted Answer

Vc(t) = V_s(1 - e^(-t/τ))

Answer

Vc(t) = V_s(1 + e^(-t/τ))

Answer

Vc(t) = V_s e^(-t/τ)

Answer

Vc(t) = V_s t/τ

Question 25

In a parallel RLC circuit, the equivalent resistance is given by:

Accepted Answer

Req = √(R^2 + (XL - Xc)^2)

Answer

Req = C/(R * L)

Answer

Req = C/(R + L)

Answer

Req = (R + L)/C

Question 26

The power factor of a series RLC circuit is given by:

Accepted Answer

PF = cos(θ)

Answer

PF = sin(θ)

Answer

PF = tan(θ)

Answer

PF = cot(θ)

Question 27

In a first-order RC circuit, derive the differential equation that governs the voltage across the capacitor. Explain the physical significance of each term in the equation.

Accepted Answer

dv/dt + (1/RC) * v = (1/C) * i

Answer

di/dt + (R/L) * i = (V/L)

Answer

d^2v/dt^2 + (R/L) * dv/dt + (1/LC) * v = 0

Answer

di/dt - (R/L) * i = (V/L)

Question 28

In an RL circuit, the current through the inductor at time t is given by I(t) = (V/R)(1 - e^(-Rt/L)). What is the rate of change of inductor current as t approaches infinity?

Accepted Answer

0

Answer

V/R

Answer

Rt/L

Answer

(V/L)e^(-t/RC)

Question 29

A capacitor with capacitance C is initially charged to voltage V0. It is then discharged through a resistor R. The time constant of this circuit is:

Accepted Answer

RC

Answer

C/R

Answer

R/C

Answer

V0RC

Question 30

An inductor with inductance L is connected in series with a battery and a switch. When the switch is closed, the initial current through the inductor is:

Accepted Answer

0

Answer

L/V

Answer

V/L

Answer

V/R

Question 31

A step voltage is applied to a series RL circuit. What is the initial voltage across the inductor?

Accepted Answer

0

Answer

V/2

Answer

V

Question 32

In a series RLC circuit, the quality factor is given by Q = ω0L/R, where ω0 is the resonant frequency. What does a low quality factor indicate?

Accepted Answer

High damping

Answer

High resonant frequency

Answer

Low resonant frequency

Answer

Low damping

Question 33

A capacitor is charged using a constant current source. The voltage across the capacitor increases linearly with time. What is the waveform of the current through the capacitor?

Accepted Answer

Constant

Answer

Sinusoidal

Answer

Parabolic

Answer

Exponential

Question 34

A 10-ohm resistor is connected in series with a 100-microfarad capacitor. The circuit is connected to a 12-volt battery. What is the initial current through the resistor?

Accepted Answer

1.2 amperes

Answer

0.12 amperes

Answer

12 amperes

Answer

2.4 amperes

Question 35

In an RL circuit, what is the effect of increasing the inductance on the time constant?

Accepted Answer

Increases

Answer

Decreases

Answer

No effect

Answer

Cannot be determined

Question 36

Which of the following is NOT a type of first-order circuit?

Accepted Answer

RLC circuit

Answer

RC circuit

Answer

LC circuit

Answer

RL circuit

Question 37

A first-order circuit is defined as having a single energy storage element. Which of the following components can store energy in a first-order circuit?

Accepted Answer

Capacitor or Inductor

Answer

Transistor

Answer

Diode

Answer

Resistor

Question 38

An initially uncharged RC circuit is suddenly connected to a DC voltage source. What happens to the capacitor's voltage?

Accepted Answer

It charges exponentially towards the applied voltage.

Answer

It remains at zero voltage.

Answer

It discharges exponentially towards the applied voltage.

Answer

It charges linearly towards the applied voltage.

Question 39

In an RL circuit, what does the inductor resist changes in?

Accepted Answer

Current

Answer

Resistance

Answer

Voltage

Answer

Capacitance

Question 40

What is the formula for the time constant (τ) of an RL circuit?

Accepted Answer

τ = L/R

Answer

τ = L + R

Answer

τ = LR

Answer

τ = L - R

Question 41

After how many time constants does a first-order circuit reach approximately 63.2% of its final steady-state value?

Accepted Answer

One time constant

Answer

Two time constants

Answer

Three time constants

Answer

Five time constants

Question 42

How does a capacitor behave in a DC circuit after a long time?

Accepted Answer

Acts like an open circuit

Answer

Has no effect on the circuit

Answer

Acts like a short circuit

Answer

Behaves like a resistor

Question 43

An inductor in a DC circuit after a long time behaves like a:

Accepted Answer

Short circuit

Answer

Resistor

Answer

Current source

Answer

Open circuit

Question 44

What is the characteristic output response of a first-order circuit when a step input is applied?

Accepted Answer

An exponential rise or fall towards a steady-state value.

Answer

A sinusoidal oscillation around a steady-state value.

Answer

A linear rise or fall towards a steady-state value.

Question 45

In a first-order low-pass filter, what defines the bandwidth?

Accepted Answer

The frequency range where the output signal is attenuated by less than 3 dB

Answer

The frequency range where the output signal remains unchanged

Answer

The frequency range where the output signal is completely blocked

Answer

The frequency range where the output signal is amplified by more than 3 dB

Question 46

If an RC circuit has a time constant of 10 ms, how long does it take for the capacitor to charge to approximately 63.2% of its final voltage?

Accepted Answer

10 ms

Answer

50 ms

Answer

20 ms

Answer

5 ms

Question 47

An RL circuit has a resistor of 100 ohms and an inductor of 10 mH. What is the time constant of this circuit?

Accepted Answer

100 µs

Answer

10 s

Answer

100 ns

Answer

1 ms

Question 48

In an RC circuit, the capacitor is initially uncharged. When the switch is closed, the current through the circuit:

Accepted Answer

Starts at a maximum value and decays exponentially to zero

Answer

Starts at zero and increases exponentially to a maximum value

Answer

Remains constant

Question 49

A first-order circuit is characterized by:

Accepted Answer

A single energy storage element (capacitor or inductor)

Answer

No energy storage elements

Answer

Multiple energy storage elements

Question 50

The steady-state response of an RC circuit with a DC source is:

Accepted Answer

The capacitor acts as an open circuit, and the voltage across the capacitor equals the source voltage.

Answer

The capacitor acts as a short circuit, and the current through the capacitor is maximum.

Question 51

In an RL circuit, the inductor acts as a(n) _____ when the switch is closed and a(n) _____ when the switch is opened.

Accepted Answer

short circuit, open circuit

Answer

open circuit, short circuit

Answer

short circuit, short circuit

Answer

open circuit, open circuit

Question 52

A 100-ohm resistor and a 10-microfarad capacitor are connected in series with a 10-volt DC source. What is the voltage across the capacitor after a long time?

Accepted Answer

10 volts

Answer

5 volts

Answer

100 volts

Answer

0 volts

Question 53

A 100 mH inductor and a 10-ohm resistor are connected in series with a 12-volt DC source. What is the current through the inductor after a long time?

Accepted Answer

1.2 A

Answer

12 A

Answer

0 A

Answer

120 A

Question 54

A first-order circuit is said to be critically damped when:

Accepted Answer

The circuit response reaches its steady-state value as quickly as possible without oscillations.

Answer

The circuit oscillates with decreasing amplitude.

Answer

The circuit oscillates with constant amplitude.

Question 55

Which of the following applications is NOT typically associated with first-order circuits?

Accepted Answer

High-frequency amplifiers

Answer

Timing circuits

Answer

Simple voltage dividers

Answer

Filters