Question

The current passing through a choke coil of $5H$ is decreasing at the rate of $2A{\text{ }}{{\text{s}}^{ - 1}}$ . The e.m.f. developed across the coil is
A. $10\,volts$
B. $- 10\,volts$
C. $2.5\,volts$
D. $- 2.5\,volts$

Answer 1

To answer this question, we must know about electromotive force (e.m.f) and its formula how an electromotive force calculated which is given by Faraday's Law, and we know that a choke coil is a choke coil is an inductance coil of exceedingly small resistance used for controlling current in an AC circuit.

Formula used:
$EMF = - L \times \dfrac{{dI}}{{dt}}$
Where, $L$ is the inductance of the coil and $\dfrac{{dI}}{{dt}}$ is the rate of change of current.

Complete step by step answer:
According to the question, the value of the inductance of the coil is $L = 5H$.
The rate of the current flow is $\dfrac{{dI}}{{dt}} = - 2A{\text{ }}{{\text{s}}^{ - 1}}$.
Here current is negative because current is decreasing.
According to Faraday’s law,
$EMF = - L \times \dfrac{{dI}}{{dt}}$
Now substituting all the values in above equation,
$EMF = - 5 \times ( - 2) \\\ \therefore EMF = 10V$

Hence, the correct option is A.

Additional information: Faraday's law of induction is a basic law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force —a phenomenon known as electromagnetic induction and a choke coil is an inductance coil of ridiculously small resistance used for controlling current in an AC circuit. In electronics, it is used to block higher frequencies while passing direct current and lower frequencies of alternating current in an electrical circuit.

Note: Do not confuse solving the question by taking the negative sign of current. In physics, the electromotive force is the maximum potential between the terminals of an electrical source. It gives energy to the charges to travel in an electric loop, which causes the current flow.