Signal Energy and Power: Interactive Quizzes for Electrical Engineering Students

Question 1

Which of these is NOT a standard unit of energy?

Accepted Answer

Kilogram-force meter

Answer

Joule

Answer

Watt-hour

Answer

Electron-volt

Question 2

Which of the following equations correctly calculates the energy of a continuous-time signal x(t) over the interval [a, b]?

Accepted Answer

E = ∫[a,b] |x(t)|^2 dt

Answer

E = ∫[a,b] x(t)^2 dt

Answer

E = ∫[a,b] |x(t)| dt

Answer

E = ∫[a,b] x(t) dt

Question 3

Which of the following is the standard unit for measuring signal power?

Accepted Answer

Watts

Answer

Joules per second

Answer

Volts

Answer

Amperes

Question 4

For a complex signal, which of the following expressions represents its average power?

Accepted Answer

E[|x(t)|^2]

Answer

E[x(t)^2]

Answer

E[|Re{x(t)}|^2]

Answer

E[Re{x(t)}^2]

Question 5

What is the mathematical expression for calculating the average power of a continuous-time signal x(t) with a finite duration?

Accepted Answer

P = (1/T) ∫[0,T] |x(t)|² dt

Answer

P = ∫[0,T] x(t)² dt

Answer

P = (1/T) ∫[0,T] x(t) dt

Question 6

Which of the following is the formula for calculating the energy of a continuous-time signal x(t) over an interval [-T/2, T/2]?

Accepted Answer

E = ∫[-T/2,T/2] |x(t)|^2 dt

Answer

E = ∫[-T/2,T/2] |x(t)| dt

Answer

E = ∫[0,T/2] |x(t)|^2 dt

Answer

E = ∫[0,T/2] |x(t)| dt

Question 7

What is the SI unit of measurement for signal power?

Accepted Answer

Watts (W)

Answer

Joules (J)

Answer

Volts (V)

Answer

Amperes (A)

Question 8

For a periodic signal with period T, what is the relationship between the average power and the signal energy per period?

Accepted Answer

Average power = Signal energy / T

Answer

Signal energy = Average power / T

Answer

Average power = Signal energy * T

Answer

Signal energy = Average power * T

Question 9

Which of the following characteristics describes a low-pass signal in terms of its energy distribution in the frequency domain?

Accepted Answer

Most of the energy is concentrated in the low-frequency range.

Answer

Most of the energy is concentrated in the high-frequency range.

Answer

The energy is equally distributed across all frequencies.

Answer

The energy is inversely proportional to the frequency.

Question 10

What is the significance of Parseval's theorem in the context of signal energy?

Accepted Answer

It relates the energy of a continuous-time signal to the energy of its Fourier transform.

Answer

It provides a method for calculating the energy of a discrete-time signal.

Answer

It states that the energy of a signal is always positive.

Answer

It is used to determine the bandwidth of a signal.

Question 11

What is the main purpose of windowing a signal before calculating its energy using a DFT?

Accepted Answer

To reduce spectral leakage and improve frequency resolution.

Answer

To increase the signal-to-noise ratio.

Answer

To determine the signal's bandwidth.

Answer

To remove DC components from the signal.

Question 12

Which of the following is the mathematical expression for signal energy? Signal energy, denoted as E, is defined as the integral of the squared magnitude of a signal x(t) over its entire duration.

Accepted Answer

E = ∫[-∞,∞) |x(t)|^2 dt

Answer

E = ∫[0,∞) |x(t)|^2 dt

Answer

E = ∫[-∞,0] |x(t)|^2 dt

Answer

E = ∫[0,∞) |x(t)| dt

Question 13

Which of the following is a unit of power?

Accepted Answer

Watts

Answer

Joules

Answer

Volts

Answer

Amperes

Question 14

Which of the following properties is associated with signal energy?

Accepted Answer

It is always positive.

Answer

It can be negative.

Answer

It is always zero.

Answer

It is only defined for periodic signals.

Question 15

Identify the correct unit of measurement for signal power.

Accepted Answer

Watts (W)

Answer

Volts (V)

Answer

Joules (J)

Answer

Hertz (Hz)

Question 16

Determine the average power of a periodic signal by applying the correct formula.

Accepted Answer

P = E/T

Answer

P = max(|x(t)|)

Answer

P is always positive

Answer

P is independent of frequency

Question 17

Which of the following signals has the greater power?

Accepted Answer

A signal with a larger amplitude and a longer duration

Answer

A signal with a larger amplitude and a shorter duration

Answer

A signal with a smaller amplitude and a shorter duration

Question 18

The energy of a periodic signal with an average power of 2W over one period is:

Accepted Answer

2 J

Answer

4 J

Answer

1 J

Question 19

Which of the following is a unit of power?

Accepted Answer

Watts

Answer

Amperes

Answer

Volts

Answer

Joules

Question 20

The power of a signal can be calculated using:

Accepted Answer

The product of the signal's voltage and current

Answer

The integral of the signal's energy over time

Answer

The square of the signal's voltage

Answer

The derivative of the signal's amplitude

Question 21

A signal with a power of 2 W and a duration of 2 seconds has an energy of:

Accepted Answer

4 J

Answer

8 J

Answer

0.5 J

Answer

2 W

Question 22

Which of the following signals has the highest energy?

Accepted Answer

A signal with a larger amplitude and a longer duration

Answer

A signal with a smaller amplitude and a shorter duration

Answer

A signal with a larger amplitude and a shorter duration

Question 23

Which of the following statements about the relationship between signal energy and signal power is incorrect?

Accepted Answer

Signal energy is always greater than or equal to signal power.

Answer

Signal energy represents the total energy contained in a signal over its entire duration.

Answer

Signal power is the average value of a signal.

Answer

The duration of a signal affects its energy and power.

Question 24

How is signal energy related to signal power?

Accepted Answer

Signal energy is the average power over the signal's entire duration.

Answer

Signal power is the highest value of the signal's amplitude.

Answer

Signal energy and signal power are unrelated concepts.

Question 25

Which of the following is the mathematical formula to calculate the energy of a continuous-time signal x(t)?

Accepted Answer

E = ∫|x(t)|^2 dt

Answer

P = lim(T→∞) (1/T) ∫|x(t)|^2 dt

Answer

E = ∫|x(t)| dt

Answer

P = ∫|x(t)|^2

Question 26

Which of the following represents the energy of a continuous-time signal x(t)?

Accepted Answer

∫[0,+∞) |x(t)|² dt

Answer

∫[0,+∞) |x(t)| dt

Answer

1/∫[0,+∞) |x(t)|² dt

Answer

max[x(t)]

Question 27

For a periodic signal with period T, what is the relationship between average power and energy?

Accepted Answer

Average power = Energy/T

Answer

Average power = Energy²*T

Answer

Average power = Energy*T

Answer

Average power = T/Energy

Question 28

For a discrete-time signal x[n], which of the following represents the energy of the signal?

Accepted Answer

Σ[n=-∞,+∞] |x[n]|²

Answer

Σ[n=-∞,+∞] x[n]

Answer

max[x[n]]

Question 29

A discrete-time signal x[n] has an energy of 20 Joules. If the signal is scaled by a factor of 2, what will be the new signal energy?

Accepted Answer

80 Joules

Answer

10 Joules

Answer

40 Joules

Answer

2 Joules

Question 30

Which of the following is a unit of signal power?

Accepted Answer

Watts (W)

Answer

Decibels (dB)

Answer

Joules (J)

Answer

Volts (V)

Question 31

A continuous-time signal x(t) has a power spectral density (PSD) of Sx(f). What does the area under the PSD curve between f1 and f2 represent?

Accepted Answer

The average power of the signal within the frequency band [f1, f2]

Answer

The total energy of the signal

Answer

The peak power of the signal

Question 32

In the context of continuous-time signals, which method is used to calculate the total energy?

Accepted Answer

Integration of the square of amplitude over the signal's duration

Answer

Computing the average value of the signal

Answer

Measuring the maximum amplitude of the signal

Question 33

For a purely sinusoidal discrete-time signal, which equation correctly defines its average power?

Accepted Answer

P = (1/2) * Amplitude^2 * Frequency

Answer

P = 2 * Amplitude * Frequency

Answer

P = Amplitude^2 + Frequency

Answer

P = Amplitude * Frequency^2

Question 34

A periodic signal has a duration of T seconds and an energy of E Joules. What is its average power?

Accepted Answer

P = E/T

Answer

P = T/E

Answer

P = E*T

Answer

P = E - T

Question 35

In an AC circuit, which quantity represents the instantaneous power delivered to a load?

Accepted Answer

Voltage * Current

Answer

Voltage - Current

Answer

Voltage^2 + Current^2

Answer

Current / Voltage

Question 36

Which type of power measurement considers the average power delivered over a complete cycle?

Accepted Answer

Active power

Answer

Apparent power

Answer

Reactive power

Answer

Complex power

Question 37

What is the typical unit of measurement for signal energy?

Accepted Answer

Joule (J)

Answer

Volt-ampere (VA)

Answer

Hertz (Hz)

Answer

Watt (W)

Question 38

Which mathematical operation is used to find the total energy of a discrete-time signal over a given interval?

Accepted Answer

Summation

Answer

Differentiation

Answer

Multiplication

Answer

Integration

Question 39

What is the mathematical formula for calculating the energy of a continuous-time signal x(t)?

Accepted Answer

∫|x(t)|²dt

Answer

∫|x(t)|dt

Answer

1/∫|x(t)|dt

Answer

1/∫|x(t)|²dt

Question 40

What is the standard unit of measurement for signal power?

Accepted Answer

Watts (W)

Answer

Hertz (Hz)

Answer

Joules (J)

Answer

Volts (V)

Question 41

Which of the following signals has the highest power?

Accepted Answer

x(t) = 2sin(t)

Answer

x(t) = -sin(t)

Answer

x(t) = sin(t)

Answer

x(t) = 0.5sin(t)

Question 42

If a signal is scaled by a factor 'k', how does its power change?

Accepted Answer

The power increases by a factor of k².

Answer

The power decreases by a factor of k².

Answer

The power remains unchanged.

Question 43

How is the average power of a random signal defined?

Accepted Answer

The expected value of its instantaneous power.

Answer

The maximum of its instantaneous power.

Answer

The minimum of its instantaneous power.

Question 44

What does the power spectral density (PSD) of a signal reveal?

Accepted Answer

The distribution of signal power across different frequencies.

Answer

The amplitude of the signal.

Answer

The total power of the signal.

Question 45

A signal x(t) has a finite energy. Which of the following is TRUE about its power?

Accepted Answer

The power of x(t) is zero.

Answer

The power of x(t) is infinite.

Answer

The power of x(t) is a non-zero constant.

Question 46

A periodic signal x(t) with period T has an average power of P. What is the power of the signal 2x(t - 1)?

Accepted Answer

4P

Answer

2P

Answer

P/2

Answer

P

Question 47

The energy of a signal x(t) is calculated by:

Accepted Answer

∫|x(t)|² dt from -∞ to ∞

Answer

lim(T→∞) (1/T) ∫x(t) dt from -T to T

Answer

lim(T→∞) (1/2T) ∫|x(t)|² dt from -T to T

Answer

∫x(t) dt from -∞ to ∞

Question 48

A signal x(t) = A cos(ωt) has a power of P. What is the power of the signal y(t) = 2A cos(ωt + φ)?

Accepted Answer

4P

Answer

2P

Answer

P/2

Answer

P

Question 49

Which of the following signals has finite energy?

Accepted Answer

A rectangular pulse of finite duration

Answer

A sinusoidal signal

Answer

A ramp signal

Answer

A DC signal

Question 50

The power of a signal x(t) is defined as:

Accepted Answer

lim(T→∞) (1/2T) ∫|x(t)|² dt from -T to T

Answer

∫x(t) dt from -∞ to ∞

Answer

∫|x(t)|² dt from -∞ to ∞

Answer

lim(T→∞) (1/T) ∫x(t) dt from -T to T

Question 51

A signal with infinite energy is classified as a(n):

Accepted Answer

Power signal

Answer

Energy signal

Answer

Periodic signal

Answer

Aperiodic signal

Question 52

The power of a signal x(t) = 2e^(-t) u(t) is:

Accepted Answer

2

Answer

0

Answer

1

Answer

∞

Question 53

Which of the following statements is NOT true about a power signal?

Accepted Answer

Its energy is finite.

Answer

It is periodic.

Answer

Its power is finite and non-zero.

Answer

It can be represented by its Fourier series.

Question 54

The energy of a signal x(t) = 5 sinc(2t) is:

Accepted Answer

5π

Answer

∞

Answer

2π

Answer

π/2