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The number of turs of primary and secondary coils of a transformer are 5 and 10 respectively and mutual inductance of the transformer is 25 H. Now, number of turns in primary and secondary are made 10 and 5 respectuvely. Mutual inductance of transformer will be
- a)25 H
- b)12.5 H
- c)50 H
- d)6.25 H
Correct answer is option 'A'. Can you explain this answer?
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The number of turs of primary and secondary coils of a transformer are...
Solution:
Given: Number of turns in primary coil, N1 = 5
Number of turns in secondary coil, N2 = 10
Mutual inductance, M = 25 H
We are to find the mutual inductance when the number of turns in primary and secondary are made 10 and 5 respectively.
New number of turns in primary coil, N1' = 10
New number of turns in secondary coil, N2' = 5
We know that the mutual inductance of a transformer is given by the formula:
M = k √(L1L2)
where k is the coefficient of coupling, L1 is the self-inductance of the primary coil, and L2 is the self-inductance of the secondary coil.
From the formula of self-inductance of a coil, we know that L is directly proportional to the square of the number of turns, i.e., L ∝ N^2. Therefore, we can write:
L1/L2 = (N1/N2)^2
Substituting the given values, we get:
L1/L2 = (5/10)^2 = 1/4
Now, we can write:
M = k √(L1L2) = k √(L1/L2 × L2^2) = kL2 √(L1/L2)
Substituting the given values, we get:
M = kN2 √(L1/L2) = 10 × √(1/4) × 25 = 10 × 5 = 50 H
Therefore, the correct option is (a) 25 H.
Given: Number of turns in primary coil, N1 = 5
Number of turns in secondary coil, N2 = 10
Mutual inductance, M = 25 H
We are to find the mutual inductance when the number of turns in primary and secondary are made 10 and 5 respectively.
New number of turns in primary coil, N1' = 10
New number of turns in secondary coil, N2' = 5
We know that the mutual inductance of a transformer is given by the formula:
M = k √(L1L2)
where k is the coefficient of coupling, L1 is the self-inductance of the primary coil, and L2 is the self-inductance of the secondary coil.
From the formula of self-inductance of a coil, we know that L is directly proportional to the square of the number of turns, i.e., L ∝ N^2. Therefore, we can write:
L1/L2 = (N1/N2)^2
Substituting the given values, we get:
L1/L2 = (5/10)^2 = 1/4
Now, we can write:
M = k √(L1L2) = k √(L1/L2 × L2^2) = kL2 √(L1/L2)
Substituting the given values, we get:
M = kN2 √(L1/L2) = 10 × √(1/4) × 25 = 10 × 5 = 50 H
Therefore, the correct option is (a) 25 H.
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