Two coils of self inductance 2 mH and 8 mH are placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is

Question

Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon:

Answer 1

To solve this problem, we need to understand the concept of mutual inductance between two coils. Mutual inductance is a measure of how much the magnetic field created by one coil induces a voltage in another coil. When the magnetic flux of one coil is completely linked with another, we can use the formula for mutual inductance:

M = \sqrt{L_1 \cdot L_2}

Where M is the mutual inductance, and L_1 and L_2 are the self-inductances of the two coils.

Given in the question:

The self-inductance of the first coil, L_1 = 2 \text{ mH}
The self-inductance of the second coil, L_2 = 8 \text{ mH}

Now, we calculate the mutual inductance using the formula:

\begin{align*} M &= \sqrt{L_1 \cdot L_2} \\ &= \sqrt{2 \times 8} \\ &= \sqrt{16} \\ &= 4 \text{ mH} \end{align*}

Thus, the mutual inductance between the coils is 4 \text{ mH}.

Therefore, the correct answer is 4 mH.

By calculating the mutual inductance, we can confirm that the option 4 mH is indeed correct, and it's confirmed that all the magnetic flux from one coil is linked with the other, leading to maximum mutual coupling.

Answer 2