Series-Parallel Combinations of Inductors

In summary, The conversation is about someone asking for help with a specific step in a problem involving resistors. They were combining two resistors incorrectly and forgetting one in parallel. The correct step is to combine the far top-right resistor with the parallel resistor second from the right. After receiving the help, they were able to solve the problem and got the correct answer.
  • #1
johnsmith7565
13
4
Homework Statement
Assume that the initial energy stored in the inductors of Fig. P6.21 is zero. Find the equivalent inductance with respect to the terminals a, b.
Relevant Equations
L(series)= L1 + L2 + ... + Ln
1/(L(parallel)) = 1/L1 + 1/L2 + ... + 1/Ln
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I am not sure where I made the mistake. If someone could point that out that would be much appreciated!
 
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  • #2
That next-to-last step on the first page looks wrong. You are combining two resisters as though they are in series and forgetting the one in parallel on the far top-right. Instead, that step should be to combine the far top-right with the parallel one second from the right.
 
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  • #3
FactChecker said:
That next-to-last step on the first page looks wrong. You are combining two resisters as though they are in series and forgetting the one in parallel on the far top-right. Instead, that step should be to combine the far top-right with the parallel one second from the right.
Thanks a million! I got the correct answer.
 
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  • #4
20 // 30 = 12
+ 8 = 20
// 80 = 16
+14 = 30
// 60 = 20
+10 = 30
// 15 = 10
+ 5 = 15 H
 

FAQ: Series-Parallel Combinations of Inductors

What is a series-parallel combination of inductors?

A series-parallel combination of inductors is a circuit arrangement where inductors are connected in both series and parallel configurations. This allows for a more complex inductor network that can have different characteristics than a single inductor.

What is the difference between series and parallel connections of inductors?

In a series connection, inductors are connected end-to-end, meaning the current flowing through one inductor also flows through the other. In a parallel connection, inductors are connected side-by-side, meaning the voltage across each inductor is the same.

How does a series-parallel combination affect the inductance of the circuit?

The inductance of a series-parallel combination is affected by the individual inductances and the arrangement of the inductors. In a series connection, the total inductance is equal to the sum of the individual inductances. In a parallel connection, the total inductance is less than the smallest individual inductance.

What is the purpose of using a series-parallel combination of inductors?

A series-parallel combination allows for more flexibility in designing circuits with specific inductance values. It also allows for the creation of more complex inductor networks that can have different characteristics than a single inductor.

How do you calculate the total inductance of a series-parallel combination?

To calculate the total inductance, you must first determine the arrangement of the inductors (series or parallel). For a series connection, simply add the individual inductances. For a parallel connection, use the formula 1/L(total) = 1/L1 + 1/L2 + 1/L3... where L1, L2, L3, etc. are the individual inductances. Then, take the reciprocal of the result to get the total inductance.

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