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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...
Given:
Number of turns in primary coil, N1 = 5
Number of turns in secondary coil, N2 = 10
Mutual inductance, M = 25 H
New Number of turns in primary coil, N1’ = 10
New Number of turns in secondary coil, N2’ = 5

To find:
Mutual inductance of the transformer, M’

Solution:
According to the formula for mutual inductance,

M = (N1*N2)*√(L1*L2)

where L1 and L2 are the self-inductances of primary and secondary coils respectively.

So,

M = (5*10)*√(L1*L2)

Squaring both sides,

M^2 = 500L1L2 …(i)

Now, when the number of turns in primary and secondary coils are changed to N1’ and N2’ respectively, the new self-inductances will be L1’ and L2’ respectively.

According to the formula for self-inductance,

L = (N^2 * μ * A) / l

where N is the number of turns, A is the cross-sectional area of the coil, l is the length of the coil and μ is the permeability of the medium.

Since the geometry of the coil and the medium remain the same, we can say that L1/L1’ = (N1’/N1)^2 and L2/L2’ = (N2’/N2)^2

Therefore, L1L2 = L1’L2’ * (N1N2 / N1’N2’) …(ii)

Substituting equation (ii) in equation (i),

M^2 = 500L1’L2’ * (N1N2 / N1’N2’)

Or, M’^2 = 500L1’L2’ * (N1’N2’ / N1N2)

Substituting the given values we get,

M’^2 = 500 * 10 * 5

M’^2 = 25000

Taking the square root of both sides,

M’ = 25 H

Therefore, the mutual inductance of the transformer when the number of turns in primary and secondary coils are changed to 10 and 5 respectively, is 25 H.
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Community Answer
The number of turs of primary and secondary coils of a transformer are...
Mutual induction inductance has a factor of multiplication of number of coils of both secondary and primary .
since we have been Knowing that multiplication is commutative by law ,so n1*n2=n2*n1
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A thermal power plant produces electric power of 600 kW at 4000 V, which is to be transported to a place 20 km away from the power plant for consumers usage. It can be transported either directly with a cable of large current carrying capacity or by using a combination of step-up and step-down transformers at the two ends. The drawback of the direct transmission is the large energy dissipation. In the method using transformers, the dissipation is much smaller. In this method , a step-up transformer is used at theplant side so that the current is reduced to a smaller value. At the consumers end, a step-down transformer is used to supply power to the consumers at the specified lower voltage. It is reasonable to assume that the power cable is purely resistive and the transformers are ideal with power factor unity. All the currents and voltages mentioned are rms values.Q.In the method using the transformers, assume that the ratio of the number of turns in the primary to that in the secondary in the step-up transformer is 1 : 10. If the power to the consumers has to be supplied at 200 V, the ratio of the number of turns in the primary to that in the secondary in the stepdown transformer is

ParagraphA thermal power plant produces electric power of 600 kW at 4000 V, which is to be transported to a place 20 km away from the power plant for consumers’ usage. It can be transported either directly with a cable of large current carrying capacity or by using a combination of step-up and step-down transformers at the two ends. The drawback of the direct transmission is the large energy dissipation. In the method using transformers, the dissipation is much smaller. In this method, a step-up transformer is used at the plant side so that the current is reduced to a smaller value. At the consumers’ end, a step-down transformer is used to supply power to the consumers at the specified lower voltage. It is reasonable to assume that the power cable is purely resistive and the transformers are ideal with the power factor unity. All the currents and voltage mentioned are rms values.Q.In the method using the transformers, assume that the ratio of the number of turns in the primary to that inthe secondary in the step-up transformer is 1 : 10. If the power to the consumers has to be supplied at200 V, the ratio of the number of turns in the primary to that in the secondary in the step-down transformeris

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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 bea)25 Hb)12.5 Hc)50 Hd)6.25 HCorrect answer is option 'A'. Can you explain this answer?
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