Question

ملفان متجاوران (X ، Y)، والشكل البياني يمثل العلاقة بين القوة الدافعة الكهربية المستحثة (emf2) في الملف (Y) ومعدل التغير في شدة التيار ($\frac{\Delta I_1}{\Delta t}$) المار في الملف (X).

ما قيمة معامل الحث المتبادل بين الملفين؟

• A. 0.5 H
• B. 1 H
• C. 1.5 H

Answer 1

Answer: (C)

1.5 H

Answer 2

The induced electromotive force (emf) in a coil due to the changing current in an adjacent coil is given by the formula:

$emf_2 = -M \frac{\Delta I_1}{\Delta t}$

where $emf_2$ is the induced EMF in the second coil, $M$ is the mutual inductance between the coils, and $\frac{\Delta I_1}{\Delta t}$ is the rate of change of current in the first coil.

The negative sign indicates the direction of the induced EMF (Lenz's Law), but for calculating the magnitude of mutual inductance, we consider:

$|emf_2| = M \left| \frac{\Delta I_1}{\Delta t} \right|$

Therefore, the mutual inductance $M$ can be found as the ratio of the induced EMF to the rate of change of current:

$M = \frac{|emf_2|}{\left| \frac{\Delta I_1}{\Delta t} \right|}$

The given graph plots $emf_2$ (on the y-axis) against $\frac{\Delta I_1}{\Delta t}$ (on the x-axis). The graph is a straight line passing through the origin, indicating a direct proportionality. The slope of this line represents the mutual inductance $M$.

To find the slope, we can pick any convenient point on the line. Let's choose the point where the rate of change of current is 8 A.s$^{-1}$. From the graph, at $\frac{\Delta I_1}{\Delta t} = 8 \text{ A.s}^{-1}$, the induced EMF $emf_2 = 12 \text{ V}$.

Using the formula for mutual inductance:

$M = \frac{emf_2}{\frac{\Delta I_1}{\Delta t}} = \frac{12 \text{ V}}{8 \text{ A.s}^{-1}}$

$M = 1.5 \text{ H}$

The value of the mutual inductance between the two coils is 1.5 H.