Problem

A pair of adjacent coils has a mutual inductance of $1.5 \, \mathrm{H}$. If the current in one coil changes from $0 \, \mathrm{A}$ to $20 \, \mathrm{A}$ in $0.5 \, \mathrm{s}$, determine the change in flux linkage with the other coil.

Data

• Mutual inductance: $M = 1.5 \, \mathrm{H}$
• Initial current: $I_i = 0 \, \mathrm{A}$
• Final current: $I_f = 20 \, \mathrm{A}$
• Time taken for change: $\Delta t = 0.5 \, \mathrm{s}$

To find:

• Change in magnetic flux linkage ($\Delta \Phi$).

Prerequisite Concepts

1. Faraday’s law of induction:

$$\varepsilon = \frac{\Delta \Phi}{\Delta t},$$

where:

• $\varepsilon$ is the induced e.m.f.,
• $\Delta \Phi$ is the change in magnetic flux linkage.

2. E.m.f. induced in terms of mutual inductance:

$$\varepsilon = M \frac{\Delta I}{\Delta t},$$

where:

• $M$ is the mutual inductance,
• $\Delta I = I_f - I_i$ is the change in current.

3. Relating the two equations:

$$\Delta \Phi = M \Delta I.$$

Solution

1. Use the formula for change in flux linkage:

$$\Delta \Phi = M \Delta I.$$

2. Substitute the values:

$$\Delta \Phi = 1.5 \cdot (20 - 0).$$

3. Simplify:

$$\Delta \Phi = 1.5 \cdot 20 = 30 \, \mathrm{Wb}.$$

Answer

The change in flux linkage with the other coil is:

$$\Delta \Phi = 30 \, \mathrm{Wb}.$$

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