Answer :
The value of the inductance, L1 is 255 Henry.
The transfer function of a circuit is a function of complex frequency, expressed as a ratio of two complex polynomial functions of the same frequency. It is generally represented as H(s).
Given,
Transfer Function, H(s) = -IF R = 270Now, 0.1s + 1.5 = -IF= -1.5/0.1=-15As per the question, we have to find out the value of the inductance, L1(in Henry).The impedance of the inductor L1 is L1s.
Thus, the overall impedance of the circuit is given by:
Z = R + L1s + L2s
From the circuit diagram, we can write the following equation:
H(s) = - L2s / (R + L1s + L2s)
Put the values of R, F and H(s) in the above equation to get the value of
L1: 0.1s + 1.5 = - L2s / (270 + L1s + L2s)
By taking inverse Laplace, we get:
Solve for L1: 2700 + 10L1 = 225L1 - L1²10L1 + 2700
= - 225L1 + L1²
Therefore,
L1² - 235L1 - 2700 = 0L1² - 255L1 + 20L1 - 2700
= 0L1(L1 - 255) + 20(L1 - 255)
= 0(L1 - 255)(L1 + 20)
= 0L1
= -20, 255
Since, L1 can not be negative, therefore L1 = 255
Hence, the value of the inductance, L1 is 255 Henry.
Learn more about inductance from the given link
https://brainly.com/question/7138348
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