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A circuit contains two inductors of 6.0 mH inductance in parallel placed in series with an inductor of 8.0 mH inductance. After one of the 6.0 mH inductors burns out, the repairman wants to replace all three inductors with one inductor of equivalent inductance. Assuming inductors combine in series and parallel the same way resistors do, what inductance should he use

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Kazeemsodikisola

Answer:

Check attachment for circuit diagram

And better understanding

Explanation:

Let find the equivalent inductance.

The 6mH in parallel to 6mH

Parallel connection will give

1 / Leq = 1 / L1 + 1 / L2

L1 = L2 = L = 6mH

1 / Leq = 1 / 6 + 1 / 6

1 / Leq = 2 / 6

1 / Leq = 1 / 3

Then, take reciprocal

Leq = 3 mH

Now the combInation of this parallel connection is connect in series with an 8mH inductor

Series connection is given as

Leq = L1 + L2

So, the equivalent of the parallel connection is 3mH and this will be connect in series with 8mH

Then, final inductance is

Leq = 3 + 8

Leq = 11 mH

Therefore, the repairman need to replace the element with one inductor of inductance 11 mH.

Ver imagen Kazeemsodikisola
hamzaahmeds

This question involves the concepts of inductance, series combination, and parallel combination.

The inductance to be used is found to be "11 mH".

RESULTANT INDUCTANCE

First, we will find out the resultant inductance of the two inductors connected in a parallel combination. Since it is given that inductors behave like resistors in combination. Therefore, resultant of two inductances connected in parallel combination will be:

[tex]\frac{1}{L}=\frac{1}{L_1}+\frac{1}{L_2}[/tex]

where,

  • L = resultant inductance of the two inductors in parallel combination = ?
  • L₁ = L₂ = inductance of the two inductors =  6 mH = 6 x 10⁻³ H

Therefore,

[tex]\frac{1}{L}=\frac{1}{6\ x\ 10^{-3}\ H}+\frac{1}{6\ x\ 10^{-3}\ H}\\\\[/tex]

L = 3 x 10⁻³ H = 3 mH

Now, we will calculate the total inductance of this combination in series combination with the third inductor as follows:

[tex]L_T=L+L_3=3\ mH+8\ mH\\L_T=11\ mH[/tex]

Learn more about inductance here:

https://brainly.com/question/18575018

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