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For the electrical system shown in the circuit below:

Given that \( R = 270 \), find the value of the inductance \( L_1 \) (in Henry) so that the transfer function is \( H(s) = 0.1s + 1.5 \).

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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