Class notes
Coefficient of coupling main simplified notes
- Course
- Institution
Here you will learn about coefficient of coupling in simplest possible way
[Show more]
Seller
Follow
tebogocalvinmapogo
Content preview
MCoefficient of coupling (k= L1 L2 )
• k, ratio of mutual inductance present in between the
two coils to the maximum possible value. (It shows
the extent at which two coils are coupled together)
• How to derive the value of k:
2
• Recall that self inductance, L =𝑙/𝜇𝑁𝜇
0 𝑟𝐴
• Therefore:
• two magnetically-coupled coils having N1 and N2 turns respectively
have the following individual coefficients of self-induction:
𝑁12 𝑁 22
L1 =
𝑙/𝜇0 𝜇𝑟𝐴
, L2= 𝑙/𝜇0 𝜇𝑟𝐴
…………………(i)
,• let ∅1 be flux produced by I1 amps, in coil 1:
𝐹
∅1 = R ,=𝑙/𝜇𝑁 𝜇𝐼 ֜
1 1
∅1
𝐼1
= 𝑙/𝜇𝑁𝜇
1 ……………………..(i)
0 𝑟𝐴 0 𝑟𝐴
• If a fraction (k1) of ∅1 links with coil 2, then:
∅ 𝑁1 𝑁1𝑁2 𝜇𝑟 𝜇0 𝐴𝑁2𝑁1
• M = 𝑘1 ∅𝐼1𝑁2 = 𝑘1 1 𝑁2 = 𝑘1 𝑁2 = 𝑘1 = 𝑘1 ( )
1 𝐼1 𝑙/𝜇0 𝜇𝑟𝐴 𝑙/𝜇0 𝜇𝑟𝐴 𝑙
……………………………..(ii)
Where 𝑘1 ≤ 1
• let ∅2 be flux produced by I2 amps, in coil 2:
∅2 =R𝐹 =𝑙/𝜇𝑁 𝜇𝐼
2 2 ֜ ∅𝐼 2 = 𝑙/𝜇𝑁𝜇 ……………………..(iii)
2
0 𝑟𝐴 2 0 𝑟𝐴
, • If a fraction (k2) of ∅2 links with coil 1, then:
𝑘 ∅ 𝑁
M= 2 2 1,
𝐼2
M =𝑘2 𝑙/𝜇𝑁1𝑁𝜇2 ………………(iv)
0 𝑟𝐴
Where𝑘2 ≤ 1
• Multiply (ii) and (iv) gives:
2
𝑁12 𝑁2
1 𝑘2 = 𝑘1 𝑘2L1L2
M 2=𝑘 𝑥
𝑙/𝜇0 𝜇𝑟𝐴 𝑙/𝜇0 𝜇𝑟𝐴
therefore:
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller tebogocalvinmapogo. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $7.99. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
82871 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now