Question

In the circuit shown, the cell is ideal. The coil has inductance of $4H$and zero resistance. F is a fuse of zero resistance and will blow when the current through it reaches $5A$. The switch is closed to $t = 0$. The fuse will blow
A. Almost at once
B. After $2\sec $
C. After $5\sec $
D. After $10\sec $

Answer 1

Hint:In this question, we can use Faraday’s law which states that induced voltage in a circuit is proportional to the rate of change of magnetic flux through that circuit.
Ideal cell is a cell with zero resistance. And the term zero resistance is defined as current passing through the circuit will be infinite.

Formula used:
Self-induced emf $\left( E \right)$ is proportional to the rate of change of the current $\left( I \right)$ of the circuit. $E = L\dfrac{{dI}}{{dt}}$

Complete Step by Step Answer:
We are given that at $t = 0$ the switch is closed which means the current is flowing through it. Hence, we firstly write the formula for emf (electromotive force) where $L$ is the inductance $I$ is the current flowing.
$E = L\dfrac{{dI}}{{dt}}$
$\Rightarrow dI = \dfrac{E}{L}dt$
Integrating,
$\int {dI = \int {\dfrac{E}{L}dt} } $
$\Rightarrow I = \dfrac{{Et}}{L}$
Given values $E = 2V$
$L = 4H$
$\Rightarrow I = 5A$
Substituting the above values
$5 = \dfrac{{2t}}{4}$
$\therefore t = 10\sec .$

Hence the correct option is $\left( {D} \right)$.

Additional information:
The current and magnetic flux direction are measured by the famous rule known as Fleming’s right hand rule. In the Fleming right hand rule, hold the right hand with the thumb, index finger and middle finger mutually perpendicular to each other, where the thumb represents the direction of motion, index finger direction of field and middle finger representing the direction of current.

Note:Inductor is a device which converts electric energy into magnetic energy. Basically, in the above question it is using a conductor that is wound into the coil and when the current starts flowing produces electricity which will generate a magnetic field in the circuit which indeed is the cause of emf.