Question

The flux linked with a coil at any instant t is given by: ɸ = 2t² + t - 1. The magnitude of induced emf at t = 4 s is: 

2) 11 V

3) 17 V

4) 20 V

5) 14 V​

Answer 1

Answer:

17 V

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Explanation:

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Answer 2

Answer:

The magnitude of induced emf is 17V.

Explanation:

Given the flux linked with a coil at any instant t is  $\phi = 2t^2 + t - 1$

And time, $t = 4 s$

According to Faraday's law, the magnitude of induced e.m.f, $\varepsilon$ is equal to the rate of change of magnetic flux, $\phi$ in a coil.

Mathematically written as $\varepsilon =-N\frac{d\phi}{dt}$

where N is the number of turns in the coil and negative sign gives the polarity of the induced emf.

Neglecting the sign and taking N = 1,

The magnitude of induced emf is

$\varepsilon =\frac{d\phi}{dt}$

$=\frac{d}{dt} (2t^2 + t - 1)$

$=4t+ 1~V$

At t = 4 s, the magnitude of induced emf is

$\varepsilon =4t+1=4\times 4+1=17V$

Therefore, the magnitude of induced emf is 17V.

Hence the correct answer is the 2nd option. (It is shown as 3 in options)