Transfer Function MCQ Quiz - Objective Question with Answer for Transfer Function - Download Free PDF
Last updated on Jun 26, 2025
Latest Transfer Function MCQ Objective Questions
Transfer Function Question 1:
The transfer function H(s) of the given circuit is:
Answer (Detailed Solution Below)
Transfer Function Question 1 Detailed Solution
Transfer Function Analysis of the Given Circuit:
The transfer function H(s) of an electrical circuit represents the relationship between the input and output signals in the Laplace domain. It is expressed as a ratio of the Laplace transform of the output signal to the Laplace transform of the input signal. In this problem, we aim to determine the correct transfer function of the given circuit.
Correct Option:
The correct transfer function is:
Option 2: H(s)=Rs2LRC+sL+R" id="MathJax-Element-32-Frame" role="presentation" style="position: relative;" tabindex="0">
Derivation:
To derive the transfer function, we analyze the circuit using fundamental principles such as Kirchhoff's Voltage Law (KVL) and Laplace transform techniques.
Step 1: Circuit Configuration and Parameters
The circuit under consideration is likely an RLC circuit, comprising a resistor (R), inductor (L), and capacitor (C). The configuration of the circuit determines how these components interact, influencing the transfer function. Based on the mathematical representation in the options, we assume it is a series RLC circuit.
Step 2: Applying Kirchhoff's Voltage Law (KVL)
For a series RLC circuit, KVL states that the sum of voltage drops across the resistor, inductor, and capacitor equals the applied input voltage:
Vin(t)=VR(t)+VL(t)+VC(t)" id="MathJax-Element-33-Frame" role="presentation" style="position: relative;" tabindex="0">
Using the Laplace transform, the voltage drops can be expressed as:
- VR(s)=RI(s)" id="MathJax-Element-34-Frame" role="presentation" style="position: relative;" tabindex="0">
VR(s)=RI(s) VR(s)=RI(s) - VL(s)=sLI(s)" id="MathJax-Element-35-Frame" role="presentation" style="position: relative;" tabindex="0">
VL(s)=sLI(s) VL(s)=sLI(s) - VC(s)=I(s)sC" id="MathJax-Element-36-Frame" role="presentation" style="position: relative;" tabindex="0">
VC(s)=I(s)sC VC(s)=I(s)sC
Substituting these into the KVL equation:
Vin(s)=RI(s)+sLI(s)+I(s)sC" id="MathJax-Element-37-Frame" role="presentation" style="position: relative;" tabindex="0">
Factorizing I(s)" id="MathJax-Element-38-Frame" role="presentation" style="position: relative;" tabindex="0">
Vin(s)=I(s)(R+sL+1sC)" id="MathJax-Element-39-Frame" role="presentation" style="position: relative;" tabindex="0">
I(s)=Vin(s)R+sL+1sC" id="MathJax-Element-40-Frame" role="presentation" style="position: relative;" tabindex="0">
Step 3: Output Voltage Relation
The output voltage is typically taken across one of the components. Based on the options provided, the output voltage is likely across the resistor. Therefore:
Vout(s)=VR(s)=RI(s)" id="MathJax-Element-41-Frame" role="presentation" style="position: relative;" tabindex="0">
Substituting I(s)" id="MathJax-Element-42-Frame" role="presentation" style="position: relative;" tabindex="0">
Vout(s)=R⋅Vin(s)R+sL+1sC" id="MathJax-Element-44-Frame" role="presentation" style="position: relative;" tabindex="0">
Thus, the transfer function H(s)" id="MathJax-Element-45-Frame" role="presentation" style="position: relative;" tabindex="0">
H(s)=Vout(s)Vin(s)=RR+sL+1sC" id="MathJax-Element-46-Frame" role="presentation" style="position: relative;" tabindex="0">
Simplify the denominator:
H(s)=Rs2LRC+sL+R" id="MathJax-Element-47-Frame" role="presentation" style="position: relative;" tabindex="0">
This matches Option 2, confirming its correctness.
Important Information:
To further analyze the other options, let’s evaluate their mathematical expressions:
Option 1: H(s)=Cs2L+sLRC+R" id="MathJax-Element-48-Frame" role="presentation" style="position: relative;" tabindex="0">
This option incorrectly places C" id="MathJax-Element-49-Frame" role="presentation" style="position: relative;" tabindex="0">
Option 3: H(s)=Rs2L+sLRC+R" id="MathJax-Element-51-Frame" role="presentation" style="position: relative;" tabindex="0">
Although this option has R" id="MathJax-Element-52-Frame" role="presentation" style="position: relative;" tabindex="0">
Option 4: H(s)=Cs2LRC+sL+R" id="MathJax-Element-54-Frame" role="presentation" style="position: relative;" tabindex="0">
This option swaps R" id="MathJax-Element-55-Frame" role="presentation" style="position: relative;" tabindex="0">
Conclusion:
The correct transfer function for the given circuit is H(s)=Rs2LRC+sL+R" id="MathJax-Element-58-Frame" role="presentation" style="position: relative;" tabindex="0">
Transfer Function Question 2:
Two systems S1 and S2 are connected in cascade and S1 is described as
Answer (Detailed Solution Below)
Transfer Function Question 2 Detailed Solution
System 1:
By applying the Laplace transform,
Y(s) = s x(s) + 2 x(s)
⇒ H1(s) = s + 2
System 2:
The transfer function of high pass filter is,
τ = RC = 1 sec
Both the systems are connected in cascade connection.
H(s) = H1(s) H2(s)
x(t) = e-2t
⇒ y(t) = δ(t) – e-t u(t)
Transfer Function Question 3:
The input 𝑥(𝑡) to a system is related to its output 𝑦(𝑡) as
Here 𝑢(𝑡) represents a unit-step function.
The transfer function of this system is ________
Answer (Detailed Solution Below)
Transfer Function Question 3 Detailed Solution
Calculation
The transfer function is defined as the ratio of the Laplace transform of output to the Laplace transform of the input keeping initial conditions zero.
Given,
where, y(t) = Output
x(t) = Input
Taking Laplace on both sides:
Transfer Function Question 4:
The roots of a system having a transfer function
Answer (Detailed Solution Below)
Transfer Function Question 4 Detailed Solution
Concept:-
The transistor function is given by =
Where K = dc gain Z1, Z2,--- = zeros
P1, P2, --- = Pole location
Calculation:
The roots of the transfer function is -3, -4.
Transfer Function Question 5:
The unique model of a system is
Answer (Detailed Solution Below)
Transfer Function Question 5 Detailed Solution
Transfer Function:
- The transfer function of a system is defined as the ratio of the Laplace transform of output to the Laplace transform of input where all the initial conditions are zero.
- The transfer function for the system is unique & it is applicable only for linear time-invariant (LTI) systems.
Signal flow graphs:
- Signal flow graphs are used to find the transfer function of the control system by converting the block diagrams into signal flow graphs
- It cannot be used for nonlinear systems.
Block diagrams:
- A block diagram is used to represent a control system in diagram form.
- Each element of the control system is represented with a block and the block is the symbolic representation of the transfer function of that element.
State variables:
- A state variable is one of the sets of variables that are used to describe the mathematical "state" of a dynamical system.
- The state variable method is used for analysis of time-variant systems.
Top Transfer Function MCQ Objective Questions
The impulse response of the transfer function 1 is
Answer (Detailed Solution Below)
Transfer Function Question 6 Detailed Solution
Download Solution PDFConcept:
- The impulse response of any system is known as the transfer function.
- The transfer function is defined as the ratio of the Laplace transform of the output to the Laplace transform of the input by assuming initial conditions to be zero.
Explanation:
T.F. =
T.F. =
Taking Inverse Laplace on both sides:
A unity feedback control system has
The order and type of the closed-loop system will be:
Answer (Detailed Solution Below)
Transfer Function Question 7 Detailed Solution
Download Solution PDFConcept:
Poles of closed-loop system = zeroes of the characteristic equation.
Characteristic equation is given by:
1 + G(s) H(s) = 0
Order: Highest power of characteristic equation.
Type: It is obtained by observing the number of open loop poles occuring at origin.
Analysis:
H(s) = 1
The characteristic equation will be:
s2 (sT + 1) + k = 0
s3 T + s2 + k = 0
The highest power of the above characteristic equation is 3
So, order = 3
Type = 2
Consider a system with the closed loop transfer function
Answer (Detailed Solution Below)
Transfer Function Question 8 Detailed Solution
Download Solution PDFConcept:
Consider a second-order control system with unity feedback:
Closed-loop transfer function is given by
where,
C(s) = Output response of CLTF
R(s) = Input to the system
ωn = Undamped natural frequency in rad/sec
ζ = Damping ratio
Application:
Given:
Input R(t) = δ(t) implies R(s) = 1,
Closed Loop Transfer function
Substitute R(s) = 1 in above CLTF, We get
Taking Inverse Laplace Transform on both sides,
C(t) = 10 e-3t u(t) + 10 e-5t u(t)
C(t) = 10 (e-3t + e-5t) u(t)
The impulse response of a system described by the differential equation
Answer (Detailed Solution Below)
Transfer Function Question 9 Detailed Solution
Download Solution PDFConcept:
A transfer function is defined as the ratio of the Laplace transform of the output to the Laplace transform of the input by assuming initial conditions are zero.
TF = L[output]/L[input]
For unit impulse input i.e. r(t) = δ(t)
⇒ R(s) = δ(s) = 1
Now transfer function = C(s)
Therefore, the transfer function is also known as the impulse response of the system.
Transfer function = L[IR]
IR = L-1 [TF]
Calculation:
By aplying the Laplace transform,
s2 Y(s) + Y(s) = X(s)
Impulse response will be the inverse Laplace transform of the above transfer function.
By applying the inverse Laplace transform,
⇒ y(t) = sin t
Therefore, the impusle response of the gien system is a sinusoid.
A linear system with H(s) = 1/s is excited by a unit step function input. The output for t > 0 is given by
Answer (Detailed Solution Below)
Transfer Function Question 10 Detailed Solution
Download Solution PDFConcept:
A transfer function is defined as the ratio of Laplace transform of the output to the Laplace transform of the input by assuming initial conditions are zero.
TF = L[output] / L[input]
So that transfer function of the system is used to calculate the output for a given input.
For unit impulse input i.e. r(t) = δ(t)
⇒ R(s) = δ(s) = 1
Now transfer function = C(s)
Therefore, transfer function is also known as impulse response of the system.
Transfer function = L[IR]
IR = L-1 [TF]
Application:
Given-
TF = H(s) = 1/s,
Input is unit step, R(s) = 1/s
Now output for t > 0 can be calculated as
C(s) = H(s) x R(s)
C(s) = (1/s) x (1/s)
C(s) = 1 / s2
L-1[C(s)] = t
C(t) = t = ramp function
A function y(t) satisfies the following differential equation:
Where δ(t) is unit impulse function and u(t) is unit step function. Assuming zero initial conditions, what is y(t)?
Answer (Detailed Solution Below)
Transfer Function Question 11 Detailed Solution
Download Solution PDFConcept:
A transfer function is defined as the ratio of Laplace transform of the output to the Laplace transform of the input by assuming initial conditions are zero.
TF = L[output]/L[input]
For unit impulse input i.e. r(t) = δ(t)
⇒ R(s) = δ(s) = 1
Now transfer function = C(s)
Therefore, the transfer function is also known as the impulse response of the system.
Transfer function = L[IR]
IR = L-1 [TF]
Calculation:
Given differential equation is,
⇒ sY(s) + Y(s) = 1
⇒ y(t) = e-t u(t)
For the closed-loop system shown, the transfer function
Answer (Detailed Solution Below)
Transfer Function Question 12 Detailed Solution
Download Solution PDFGiven:
Forward path gain = G
Feedback path gain = H
Input signal = R(s)
Output signal = C(s)
Error signal = E(s)
C(s) = G × E(s)
Error signal = Input signal - Feedback signal
E(s) = R(s) - H × C(s)
E(s) = R(s) - H × G × E(s)
E(s) + H × G × E(s) = R(s)
E(s) [1 + GH] = R(s)
Find the overall transfer function for the following system.
Answer (Detailed Solution Below)
Transfer Function Question 13 Detailed Solution
Download Solution PDFBy using the block-reduction technique:
Step 1:
Blocks having value 2 and
Step 2:
Blocks having value
Step 3:
Noe its a negative UFB system:
The transfer function of a system is given by,
Let the output of the system be
Answer (Detailed Solution Below)
Transfer Function Question 14 Detailed Solution
Download Solution PDFTransfer function,
Vi (t) = Vm sin(ωt)
Vo (t) = Vm sin(ωt + ϕ)
Here, ϕ = tan-1 (-ω) - tan-1(ω)
= - tan1(ω) - tan-1 (ω)
= - 2 tan-1(ω)
At ω = 0,
⇒ ϕ = - 2 tan-1(0) = 0 (since tan-1(0) = 0 )
At ω = ∞,
⇒ - 2 tan-1(∞) = - 2 × π/2 = - π (since tan-1(∞) = π/2)
Range of ϕ = (-π, 0)
The unique model of a system is
Answer (Detailed Solution Below)
Transfer Function Question 15 Detailed Solution
Download Solution PDFTransfer Function:
- The transfer function of a system is defined as the ratio of the Laplace transform of output to the Laplace transform of input where all the initial conditions are zero.
- The transfer function for the system is unique & it is applicable only for linear time-invariant (LTI) systems.
Signal flow graphs:
- Signal flow graphs are used to find the transfer function of the control system by converting the block diagrams into signal flow graphs
- It cannot be used for nonlinear systems.
Block diagrams:
- A block diagram is used to represent a control system in diagram form.
- Each element of the control system is represented with a block and the block is the symbolic representation of the transfer function of that element.
State variables:
- A state variable is one of the sets of variables that are used to describe the mathematical "state" of a dynamical system.
- The state variable method is used for analysis of time-variant systems.