Electrical Engineering (EE) Exam > Electrical Engineering (EE) Questions > The Laplace transform of unity function isa)1...
Start Learning for Free
The Laplace transform of unity function is
- a)1
- b)zero
- c)s
- d)1/s
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The Laplace transform of unity function isa)1b)zeroc)sd)1/sCorrect ans...
The laplace transform of unity function i.e.
Most Upvoted Answer
The Laplace transform of unity function isa)1b)zeroc)sd)1/sCorrect ans...
The Laplace transform of the unity function is 1/s.
The unity function, also known as the step function or the Heaviside function, is defined as:
u(t) = 1, t >= 0
u(t) = 0, t < />
The Laplace transform is a mathematical tool used to transform a function of time, f(t), into a function of the complex variable s. It is defined as:
F(s) = L{f(t)} = ∫[0 to ∞] e^(-st) * f(t) dt
where s is a complex number parameter and F(s) is the Laplace transform of f(t).
To find the Laplace transform of the unity function, we substitute u(t) into the Laplace transform equation:
F(s) = L{u(t)} = ∫[0 to ∞] e^(-st) * u(t) dt
Since the unity function is equal to 1 for t >= 0, the integral becomes:
F(s) = ∫[0 to ∞] e^(-st) dt
Integrating the exponential function with respect to t gives:
F(s) = [-1/s * e^(-st)] [0 to ∞]
Applying the limits of integration:
F(s) = [-1/s * e^(-s∞)] - [-1/s * e^(-s0)]
As t approaches infinity, e^(-s∞) approaches zero. Also, e^(-s0) is equal to 1. Therefore, the equation simplifies to:
F(s) = 0 - (-1/s)
F(s) = 1/s
Thus, the Laplace transform of the unity function is 1/s.
Therefore, the correct answer is option 'D'.
The unity function, also known as the step function or the Heaviside function, is defined as:
u(t) = 1, t >= 0
u(t) = 0, t < />
The Laplace transform is a mathematical tool used to transform a function of time, f(t), into a function of the complex variable s. It is defined as:
F(s) = L{f(t)} = ∫[0 to ∞] e^(-st) * f(t) dt
where s is a complex number parameter and F(s) is the Laplace transform of f(t).
To find the Laplace transform of the unity function, we substitute u(t) into the Laplace transform equation:
F(s) = L{u(t)} = ∫[0 to ∞] e^(-st) * u(t) dt
Since the unity function is equal to 1 for t >= 0, the integral becomes:
F(s) = ∫[0 to ∞] e^(-st) dt
Integrating the exponential function with respect to t gives:
F(s) = [-1/s * e^(-st)] [0 to ∞]
Applying the limits of integration:
F(s) = [-1/s * e^(-s∞)] - [-1/s * e^(-s0)]
As t approaches infinity, e^(-s∞) approaches zero. Also, e^(-s0) is equal to 1. Therefore, the equation simplifies to:
F(s) = 0 - (-1/s)
F(s) = 1/s
Thus, the Laplace transform of the unity function is 1/s.
Therefore, the correct answer is option 'D'.
|
Explore Courses for Electrical Engineering (EE) exam
|
|
Similar Electrical Engineering (EE) Doubts
Top Courses for Electrical Engineering (EE)View all
Question Description
The Laplace transform of unity function isa)1b)zeroc)sd)1/sCorrect answer is option 'D'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about The Laplace transform of unity function isa)1b)zeroc)sd)1/sCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The Laplace transform of unity function isa)1b)zeroc)sd)1/sCorrect answer is option 'D'. Can you explain this answer?.
The Laplace transform of unity function isa)1b)zeroc)sd)1/sCorrect answer is option 'D'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about The Laplace transform of unity function isa)1b)zeroc)sd)1/sCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The Laplace transform of unity function isa)1b)zeroc)sd)1/sCorrect answer is option 'D'. Can you explain this answer?.
Solutions for The Laplace transform of unity function isa)1b)zeroc)sd)1/sCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electrical Engineering (EE).
Download more important topics, notes, lectures and mock test series for Electrical Engineering (EE) Exam by signing up for free.
Here you can find the meaning of The Laplace transform of unity function isa)1b)zeroc)sd)1/sCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The Laplace transform of unity function isa)1b)zeroc)sd)1/sCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for The Laplace transform of unity function isa)1b)zeroc)sd)1/sCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of The Laplace transform of unity function isa)1b)zeroc)sd)1/sCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The Laplace transform of unity function isa)1b)zeroc)sd)1/sCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice Electrical Engineering (EE) tests.
|
|
Explore Courses for Electrical Engineering (EE) exam
|
|
Signup to solve all Doubts
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup