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When two coupled coils of equal self inductance are connected in series in one way, the net inductance is 12 mH and when they are connected in the other way, the net inductance is 4 mH. The maximum value of net inductance when they are connected in parallel In a suitable way is
- a)6mH
- b)4mH
- c)3 mH
- d)2 mH
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
When two coupled coils of equal self inductance are connected in serie...
Given,
From above two equations,
To get maximum value in parallel connections,
Most Upvoted Answer
When two coupled coils of equal self inductance are connected in serie...
L1+L2=4 .(1)
L1+L2+2M=12 .(2)
WHICH GIVES M=4
(1) IMPLIES L1=L2=2
PARALLEL COMBINATION OF SIMILAR INDUCTANCES IMPLIES Leq=(L+M)/2=(2+4)/2=3 mH
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When two coupled coils of equal self inductance are connected in serie...
Given:
- Two coupled coils of equal self-inductance
- When connected in series in one way, the net inductance is 12 mH
- When connected in series in the other way, the net inductance is 4 mH
To find:
The maximum value of the net inductance when the coils are connected in parallel in a suitable way.
Solution:
When two coils are connected in series, the net inductance is given by the formula:
1/Ls = 1/L1 + 1/L2 + 2M/√(L1 * L2)
Where Ls is the net inductance, L1 and L2 are the self-inductances of the individual coils, and M is the mutual inductance between the coils.
Case 1: Coils connected in series in one way (Ls = 12 mH)
Let's assume the self-inductance of each coil is L, and the mutual inductance between the coils is M.
1/12 = 1/L + 1/L + 2M/√(L * L)
1/12 = 2/L + 2M/L
1/12 = (2 + 2M)/L
Case 2: Coils connected in series in the other way (Ls = 4 mH)
1/4 = 1/L + 1/L - 2M/√(L * L)
1/4 = 2/L - 2M/L
1/4 = (2 - 2M)/L
By solving the above two equations, we can find the values of L and M.
Case 3: Coils connected in parallel
When two coils are connected in parallel, the net inductance Lp is given by the formula:
1/Lp = 1/L1 + 1/L2 + 2M/√(L1 * L2)
To maximize the net inductance, we need to find the maximum possible value of Lp.
From the previous equations, we have the values of L and M. Substituting these values into the formula for Lp, we get:
1/Lp = 1/L + 1/L + 2M/√(L * L)
1/Lp = 2/L + 2M/L
1/Lp = (2 + 2M)/L
Since Ls = 12 mH in one case and 4 mH in the other case, the maximum value of Lp will occur when the denominator of the above equation is minimized.
For the denominator to be minimized, the numerator (2 + 2M) should be maximized.
Therefore, the maximum value of the net inductance Lp when the coils are connected in parallel is 3 mH (option C).
- Two coupled coils of equal self-inductance
- When connected in series in one way, the net inductance is 12 mH
- When connected in series in the other way, the net inductance is 4 mH
To find:
The maximum value of the net inductance when the coils are connected in parallel in a suitable way.
Solution:
When two coils are connected in series, the net inductance is given by the formula:
1/Ls = 1/L1 + 1/L2 + 2M/√(L1 * L2)
Where Ls is the net inductance, L1 and L2 are the self-inductances of the individual coils, and M is the mutual inductance between the coils.
Case 1: Coils connected in series in one way (Ls = 12 mH)
Let's assume the self-inductance of each coil is L, and the mutual inductance between the coils is M.
1/12 = 1/L + 1/L + 2M/√(L * L)
1/12 = 2/L + 2M/L
1/12 = (2 + 2M)/L
Case 2: Coils connected in series in the other way (Ls = 4 mH)
1/4 = 1/L + 1/L - 2M/√(L * L)
1/4 = 2/L - 2M/L
1/4 = (2 - 2M)/L
By solving the above two equations, we can find the values of L and M.
Case 3: Coils connected in parallel
When two coils are connected in parallel, the net inductance Lp is given by the formula:
1/Lp = 1/L1 + 1/L2 + 2M/√(L1 * L2)
To maximize the net inductance, we need to find the maximum possible value of Lp.
From the previous equations, we have the values of L and M. Substituting these values into the formula for Lp, we get:
1/Lp = 1/L + 1/L + 2M/√(L * L)
1/Lp = 2/L + 2M/L
1/Lp = (2 + 2M)/L
Since Ls = 12 mH in one case and 4 mH in the other case, the maximum value of Lp will occur when the denominator of the above equation is minimized.
For the denominator to be minimized, the numerator (2 + 2M) should be maximized.
Therefore, the maximum value of the net inductance Lp when the coils are connected in parallel is 3 mH (option C).
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When two coupled coils of equal self inductance are connected in series in one way, the net inductance is 12 mH and when they are connected in the other way, the net inductance is 4 mH. The maximum value of net inductance when they are connected in parallel In a suitable way isa)6mHb)4mHc)3 mHd)2 mHCorrect answer is option 'C'. Can you explain this answer?
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Solutions for When two coupled coils of equal self inductance are connected in series in one way, the net inductance is 12 mH and when they are connected in the other way, the net inductance is 4 mH. The maximum value of net inductance when they are connected in parallel In a suitable way isa)6mHb)4mHc)3 mHd)2 mHCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electrical Engineering (EE).
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