The series RL circuit of Figure Q4 is subject to a unit step voltage input of height 5 volts at time t=0. The initial current in the circuit i(0) = 0. sw R (t = 0) V 5V Figure Q4 a) Take Laplace transforms and find an expression for the current flowing in the circuit I(s). b) Take inverse transforms and hence identify the time response of the current i(t). c) Use the final value theory to find an expression for the steady state current flowing in the circuit and compare your answer with that expected. d) Assuming the values of R and L are 10 Q and 2 H respectively, identify the time constant of the circuit and estimate the time required for the current to reach its final value, explaining your reasoning.
Transfer function
A transfer function (also known as system function or network function) of a system, subsystem, or component is a mathematical function that modifies the output of a system in each possible input. They are widely used in electronics and control systems.
Convolution Integral
Among all the electrical engineering students, this topic of convolution integral is very confusing. It is a mathematical operation of two functions f and g that produce another third type of function (f * g) , and this expresses how the shape of one is modified with the help of the other one. The process of computing it and the result function is known as convolution. After one is reversed and shifted, it is defined as the integral of the product of two functions. After producing the convolution function, the integral is evaluated for all the values of shift. The convolution integral has some similar features with the cross-correlation. The continuous or discrete variables for real-valued functions differ from cross-correlation (f * g) only by either of the two f(x) or g(x) is reflected about the y-axis or not. Therefore, it is a cross-correlation of f(x) and g(-x) or f(-x) and g(x), the cross-correlation operator is the adjoint of the operator of the convolution for complex-valued piecewise functions.
![The series RL circuit of Figure Q4 is subject to a unit step voltage input of height 5 volts at time
t=0. The initial current in the circuit i(0) = 0.
sw
R
(t = 0)
V
5V
Figure Q4
a) Take Laplace transforms and find an expression for the current flowing
in the circuit I(s).
b) Take inverse transforms and hence identify the time response of the
current i(t).
c) Use the final value theory to find an expression for the steady state current
flowing in the circuit and compare your answer with that expected.
d) Assuming the values of R and L are 10 Q and 2 H respectively, identify the
time constant of the circuit and estimate the time required for the current to
reach its final value, explaining your reasoning.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F67a27821-7cb0-4aaa-825b-4fd904033952%2F5fcf5c61-1bac-4d56-8396-b7792f6ae4bf%2Fajhwshq_processed.png&w=3840&q=75)
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