Animated Solution for Physics - Electromagnetic Induction: In a fluorescent lamp choke (a small transformer) 100 V of reverse voltage is produced when the choke current changes uniformly from 0.25A to 0 in a duration of 0.025 ms. The self-inductance of the choke (in mH) is estimated to be …… .

The phenomenon of self-induction is one of the most fascinating aspects of electromagnetism. It is nature's way of maintaining the status quo in an electrical circuit. In this problem, we explore the inner workings of a fluorescent lamp choke, which is essentially a tightly wound coil of wire—an inductor.

Imagine the current flowing through the choke. Suddenly, this current is forced to drop from $0.25\text{ A}$ to zero in a mere $0.025\text{ ms}$. According to Lenz's Law, the inductor despises this sudden change. It fights back by generating a "reverse voltage" to keep the current flowing.

This induced electromotive force (emf) is given as $100\text{ V}$. Our mission is to determine the self-inductance, $L$, of this choke, which measures its "electrical inertia."

The mathematical engine driving this phenomenon is Faraday's Law of Induction applied to a single coil. The magnitude of the induced emf is directly proportional to the rate of change of current:

We can rearrange this equation to isolate our target variable, the self-inductance $L$:

Before we rush into substituting the numbers, we must pause and inspect our units. Physics is unforgiving when it comes to mismatched units!

The time duration is given as $\Delta t=0.025\text{ ms}$. To use standard SI units, we must convert this to seconds:

The change in current is straightforward:

Now, we substitute our pristine, unit-corrected values into the rearranged formula:

Let's simplify the numerator first. Multiplying $100$ by $0.025$ gives us $2.5$:

Dividing $2.5$ by $0.25$ yields exactly $10$:

The question specifically asks for the answer in millihenrys ($\text{mH}$). Since $1\text{ mH}=10^{-3}\text{ H}$, we can seamlessly write our final answer: $L=10\text{ mH}$

This elegant result shows how a relatively small inductance can produce a massive $100\text{ V}$ spike if the current is interrupted rapidly enough!