Question

Two coils of self inductances \(2 \mathrm{mH} \& 8 \mathrm{mH}\) are placed so close together that the effective flux in one coil is completely half with the other. The mutual inductance between these coils is...... (a) \(4 \mathrm{mH}\) (b) \(6 \mathrm{mH}\) (c) \(2 \mathrm{mH}\) (d) \(16 \mathrm{mH}\)

Short answer

The mutual inductance between these coils is \(2 \, mH\).

Step-by-step solution

Write down the given information

We are given the self inductances of the two coils: \(L_1 = 2 \, mH\) \(L_2 = 8 \, mH\) And we are given that the effective flux in one coil is completely half with the other, so the coefficient of coupling between the coils, k, is 0.5.

Calculate the theoretical maximum mutual inductance

The theoretical maximum mutual inductance (Mi_max) between two coils can be calculated using the square root of the product of their self inductances: \(M_i_{max} = \sqrt{L_1 \cdot L_2}\) Plugging in the values, we get: \(M_i_{max} = \sqrt{2 \cdot 8} = \sqrt{16} = 4 \, mH\)

Calculate the mutual inductance

Now we will use the formula for the mutual inductance (Mi) which is given by the product of the coefficient of coupling (k) and the theoretical maximum mutual inductance (Mi_max): \(M_i = k \cdot M_i_{max}\) Plugging in the values, we get: \(M_i = 0.5 \cdot 4 = 2 \, mH\) So, the mutual inductance between these coils is 2 mH. Therefore, the correct answer is (c) 2 mH.