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Test: Properties of Systems - Electrical Engineering (EE) MCQ


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20 Questions MCQ Test Signals and Systems - Test: Properties of Systems

Test: Properties of Systems for Electrical Engineering (EE) 2024 is part of Signals and Systems preparation. The Test: Properties of Systems questions and answers have been prepared according to the Electrical Engineering (EE) exam syllabus.The Test: Properties of Systems MCQs are made for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Properties of Systems below.
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Test: Properties of Systems - Question 1

Construct the inverse system of y(t) = 2x(t)

Detailed Solution for Test: Properties of Systems - Question 1

Now, y(t) = 2x(t) => x(t) = 0.5y(t)
Thus, reversing x(t) <-> y(t), we obtain the inverse system: y(t) = 0.5x(t)

Test: Properties of Systems - Question 2

Which of the following is an intensive property?

Detailed Solution for Test: Properties of Systems - Question 2

Concept:

  • Properties
  • All measurable characteristics of a system are known as properties.
  • Eg. Pressure, volume, temperature, internal energy, density etc.
  • There are two types of properties:


Explanation:
Pressure:

  • Intensive properties are properties that do not depend on the quantity of matter. For example, pressure and temperature are intensive properties so the correct answer is option 3.

Entropy:

  • Entropy in classical thermodynamics is an extensive quantity, which like energy, volume, or particle number, is additive when systems in equivalent thermodynamic states are aggregated.

Volume:

  • Volume is the amount of space an object takes up, it is denoted by V.
  • Volume depends on the mass of the substance as the formula for volume is :

  • We see that volume is the ratio of two intensive properties. It is thus an extensive property.

Additional Information

Enthalpy:

  • It is defined as the amount of heat change during a chemical reaction denoted by 'H'.
  • It is given by:

H = U + PΔ V, where H = Enthalpy, U = Internal Energy, P = Pressure, V = Volume.

  • The unit of enthalpy is Joule/mole, which signifies that it depends on the amount of substance present.
  • Thus, Enthalpy is an extensive property.

Energy:

  • Internal energy is the sum of all the types of energy present in the system, such as kinetic energy, potential energy, vibrational energy, rotational energy, etc.
  • It is denoted by U and given by the formula:

​dU = q + w, where q is the heat absorbed and w is work done.

  • The unit of Internal energy is Joule/mole, which signifies that it depends on the amount of substance present.
  • Thus, Energy is an Extensive property.

Temperature:

  • Temperature(T) is the measurement of the heat content of a body.
  • It,s units are Celcius (0C), Kelvin (K), Farhenheit (0F).
  • The temperature of a body does not depend on the amount of mass of a substance. If gas has say temperature 288K, it will mean that every particle of the gas is at a temperature of 288K. It is thus an intensive property.

Hence, the intensive property is Temperature.

Test: Properties of Systems - Question 3

Comment on the linearity of y[n] = n*x[n].

Detailed Solution for Test: Properties of Systems - Question 3

The function obeys the scaling/homogeneity property, but doesn’t obey the additivity property, thus not being linear.

Test: Properties of Systems - Question 4

 y(t) = x2(t). Is y(t) = sqrt(x(t)) the inverse of the first system?

Detailed Solution for Test: Properties of Systems - Question 4

B. No

- The inverse of a system is a system that undoes the operation of the original system.
- In the given system, y(t) is equal to the square of x(t), y(t) = x2(t).
- If we take the square root of y(t) to find the inverse, we get y(t) = √(x(t)).
- However, √(x(t)) is not equal to x(t), so it does not undo the operation of squaring x(t).
- Therefore, y(t) = √(x(t)) is not the inverse of the given system.
- Hence, the correct answer is B: No.

Test: Properties of Systems - Question 5

Comment on the causality of y[n] = x[-n].

Detailed Solution for Test: Properties of Systems - Question 5

For positive time, the system may seem to be causal. However, for negative time, the output depends on time at a positive sign, thus being in the future, enforcing non causality.

Test: Properties of Systems - Question 6

 y[t]= ∫x[t],t ranges from 0 to t. Is the system a memoryless one?

Detailed Solution for Test: Properties of Systems - Question 6

While evaluating the integral, it becomes imperative to know the values of x[t] from 0 to t, thus making the system requiring memory.

Test: Properties of Systems - Question 7

y(t) = x(t)2. Is y(t) = sqrt(x(t)) the inverse of the first system?

Detailed Solution for Test: Properties of Systems - Question 7

We cannot determine the sign of the input from the second function, thus, the output doesn’t replicate the input. Thus, the second function is not an inverse of the first one.

Test: Properties of Systems - Question 8

y(t) = sin(x(t-1)) : Comment on its memory aspects.

Detailed Solution for Test: Properties of Systems - Question 8

The output at any time t = A, requires knowing the input at an earlier time, t = A – 1, hence making the system require memory aspects.

Test: Properties of Systems - Question 9

 y(t) = x(t-2) + x(2-t). Comment on its causality:

Detailed Solution for Test: Properties of Systems - Question 9

For a time instant existing between 0 and 1, it would depend on the input at a time in the future as well, hence being non causal.

Test: Properties of Systems - Question 10

Given the systems (i) y(n) = n x(n) and (ii) y(n) = ex(n)

Detailed Solution for Test: Properties of Systems - Question 10

Concept: Linearity: Necessary and sufficient condition to prove the linearity of the system is that linear system follows the laws of superposition i.e. the response of the system is the sum of the responses obtained from each input considered separately.

y{ax1[n] + bx2[t]} = a y{x1[n]} + b y{x2[n]}

Conditions to check whether the system is linear or not.

  1. The output should be zero for zero input
  2. There should not be any non-linear operator present in the system

Causality: A system is causal, if the output of the system does not depend on future inputs, but only on past input.

Time-Invariance: If the input to a time-invariant system is shifted in time, its output remains the same signal, but is shifted equally in time.

If the output for an input x(t) is y(t), then for a time shift of t0 in the input gives the t0 shift in the output.

x(t) → y(t), then x(t – t0) → y(t – t0)

Application:

(i) y(n) = n x(n)

Here in the system, there is a nonlinear operator and hence it is linear.

(ii) y(n) = ex(n)

Here there is a non-linear operator (exponential) and hence it is nonlinear.

Test: Properties of Systems - Question 11

Specific enthalpy is an ________ of a system and its unit is ________.

Detailed Solution for Test: Properties of Systems - Question 11

Properties of Systems Question 4 Detailed Solution
Intensive Property: These are the properties of system which are independent of mass under consideration. For e.g. Pressure (Pa), Temperature (K), density (kg/m3), specific enthalpy (kJ/kg)
Extensive Properties: The properties which depend on the mass of system under consideration.
For e.g. Internal Energy (kJ), Enthalpy (kJ), Volume (m3), Entropy (kJ)

Note: All specific properties are intensive properties. For e.g. specific volume, specific entropy, specific enthalpy etc.
Thus, Specific enthalpy (enthalpy per unit mass) is an intensive property and its unit is kJ/kg.

Test: Properties of Systems - Question 12

 What is the following type of system called? y[n] = x[n] + y[n-1].

Detailed Solution for Test: Properties of Systems - Question 12

If we write for n-1, n-2, .. we will obtain y[n] = x[n] + x[n-1] + x[n-2] …,
thus obtaining an adder system.

Test: Properties of Systems - Question 13

 Which of the following systems is stable?

Detailed Solution for Test: Properties of Systems - Question 13

Stability implies that a bounded input should give a bounded output. In a, b, d there are regions of x, for which y reaches infinity/negative infinity. Thus the sin function always stays between -1 and 1, and is hence stable.

Test: Properties of Systems - Question 14

Which of the following systems is time invariant?

Detailed Solution for Test: Properties of Systems - Question 14

In each of b and c there is a negative sign of t involved, which means a backward shift of t-0 in time, would mean a forward shift in each of them. In option a twice of t leads to time variant. However, only in d, the backward shift will remain as backward, and undiminished.

Test: Properties of Systems - Question 15

Which property of delta function indicates the equality between the area under the product of function with shifted impulse and the value of function located at unit impulse instant ?

Detailed Solution for Test: Properties of Systems - Question 15

Sampling  indicates the equality between the area under the product of function with shifted impulse and the value of function located at unit impulse instant

Test: Properties of Systems - Question 16

 y(t) = x(t-2) + x(2-t). Comment on its causality:

Detailed Solution for Test: Properties of Systems - Question 16

 For a time instant existing between 0 and 1, it would depend on the input at a time in the future as well, hence being non causal.

Test: Properties of Systems - Question 17

Which of the following systems is memoryless?

Detailed Solution for Test: Properties of Systems - Question 17

A system possessing no memory has its output depending upon the input at the same time instant, which is prevalent only in option b.

Test: Properties of Systems - Question 18

 For what value of k, will the following system be time invariant?

y(t) = x(t) + x(kt) – x(2t) + x(t-1)

Detailed Solution for Test: Properties of Systems - Question 18

Here, when we put k=2

=> y(t) = x(t) + x(2t) – x(2t) + x(t-1)

=> y(t) = x(t) + x(t-1)

As we need to eliminate the term x(2t) to make the system time invariant, the value of k must be 2.

Therefore, the correct answer is B.

Test: Properties of Systems - Question 19

What is the following type of system called? y[n] = x[n] + y[n-1].

Detailed Solution for Test: Properties of Systems - Question 19

 If we write for n-1, n-2, .. we will obtain y[n] = x[n] + x[n-1] + x[n-2] …,
thus obtaining an adder system.

Test: Properties of Systems - Question 20

Which of the following systems is time invariant?

Detailed Solution for Test: Properties of Systems - Question 20

In each of a, b and c there is a negative sign of t involved, which means a backward shift of t-0 in time, would mean a forward shift in each of them. However, only in d, the backward shift will remain as backward, and undiminished.

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