Question

In a fluorescent lamp choke (a small transformer) 100 V of reversible voltage is produced when the choke changes current from 0.25 A to 0 A in 0.025 ms. Find the self-inductance of the choke (in mH).

Answer 1

Hint: In this question, we need to find the self-inductance of choke in mH. For this, we have to use Faraday’s law for the induced emf. We will use the following formula for the induced emf to solve this example.

Formula used:
According to Faraday’s law, the formula for the induced emf is given below.
\[{E_{induced}} = L \times \dfrac{{dI}}{{dt}}\]
Here, L is the inductance and \[\dfrac{{dI}}{{dt}}\] is change in current with respect to time t.
This gives
\[L = \dfrac{{{E_{induced}} \times \vartriangle t}}{{\vartriangle I}}\]
Here, \[{E_{induced}}\] is induced emf, \[\vartriangle t\] is the change in time and \[\vartriangle I\] is the change in electric current.

Complete step by step solution:
According to Faraday’s law, the inductance from the choke is given by
\[L = \dfrac{{{E_{induced}} \times \vartriangle t}}{{\vartriangle I}}\] ….. (1)
But \[{E_{induced}} = 100{\text{ V}}\]
Also, \[\vartriangle I = 0.25 - 0 = 0.25{\text{ A}}\]
\[\vartriangle t = 0.025{\text{ }}ms\]
Let us convert the above time in seconds.
So, \[1{\text{ ms}} = {10^{ - 3}}s\]
Thus, we get
\[\vartriangle t = 0.025 \times {10^{ - 3}}{\text{ }}s\]

So, from equation (1), we get
\[L = \dfrac{{100 \times 0.025 \times {{10}^{ - 3}}}}{{0.25}}\]
By simplifying, we get
\[L = \dfrac{{{{10}^2} \times 0.25 \times {{10}^{ - 1}} \times {{10}^{ - 3}}}}{{0.25}}\]
\[\Rightarrow L = {10^2} \times {10^{ - 1}} \times {10^{ - 3}}\]
\[\Rightarrow L = {10^{2 - 4}}\]
\[\Rightarrow L = {10^{ - 2}}\]
Let us make it simple.
\[L = 10 \times {10^{ - 3}}\]
That means, \[L = 10\]mH
Hence, the value of the self-inductance of the choke is 10 mH.

Therefore, the self-inductance of the choke is 10 mH.

Additional information: An electromotive force is induced whenever the coil's current or magnetic flux changes. Self-Inductance is the name given to this concept. Once current begins to flow through the coil at any time, the magnetic flux has become directly proportional to the current flowing through the circuit.

Note: Many students generally make mistakes in writing the formula of induced emf that is based on faraday's law. Also, they may forget to convert milliseconds into seconds. As a result, the end value may get wrong. Here, the calculation for self-inductance plays a significant role.