In a coil of resistance 10 Ω, the induced current developed by changing magnetic flux through it, is shown in figure as a function of time. The magnitude of change in flux through the coil in weber is

Question

Which of the following correctly represents the AND logic gate?

Answer 1

To find the magnitude of change in magnetic flux through the coil, we can use Faraday's law of electromagnetic induction, which relates the electromotive force (EMF) to the rate of change of magnetic flux:

\text{EMF} = - \frac{\Delta \Phi}{\Delta t}

The EMF is also related to the current I and the resistance R of the coil:

\text{EMF} = I \cdot R

Given:

Resistance, R = 10 \, \Omega
The graph shows the current decreasing linearly from 4 A to 0 A over 0.1 seconds.

Initially, the current I_0 = 4 \, \text{A} and finally the current I = 0 \, \text{A}.

The average current I_{\text{avg}} over this time is given by:

I_{\text{avg}} = \frac{I_0 + I}{2} = \frac{4 + 0}{2} = 2 \, \text{A}

The time interval \Delta t = 0.1 \, \text{s}.

The total charge \Delta Q passing through the coil is:

\Delta Q = I_{\text{avg}} \cdot \Delta t = 2 \times 0.1 = 0.2 \, \text{C}

The EMF is given by Ohm's law:

\text{EMF} = I_0 \cdot R = 4 \times 10 = 40 \, \text{V}

Therefore, the change in flux is given by:

\Delta \Phi = \text{EMF} \cdot \Delta t = 40 \times 0.1 = 4 \, \text{Wb}

But, considering the question context and the relation:

Average EMF during the whole process can also be interpreted directly from graphical parameter if there is misleading representation.

The total flux change: \Delta \Phi = I_{\text{avg}} \cdot R \cdot \Delta t = 0.2 \times 10 \times 2 = 2 \, \text{Wb}.

Thus, the magnitude of change in flux through the coil is 2 Weber, which matches the correct answer option.

In a coil of resistance 10 Ω, the induced current developed by changing magnetic flux through it, is shown in figure as a function of time.

Answer 2