Q142 / 180 · COMEDK 2023 (Memory Based) · Physics

The magnetic flux linked with a coil satisfies the relation $\phi=\left(4 t^2+6 t+9\right) \mathrm{Wb}$, where $t$ is time in second. The emf induced in the coil at $t=2 \mathrm{~s}$ is

  • Correct answer
    A
    $22 \mathrm{~V}$
  • B
    $18 \mathrm{~V}$
  • C
    $16 \mathrm{~V}$
  • D
    $40 \mathrm{~V}$

Solution

Given, $\phi=\left(4 t^2+6 t+9\right) \mathrm{Wb}$ and $t=2 \mathrm{~s}$ We know that, $|\varepsilon|=\left|\frac{d \phi}{d t}\right|$ Here, $\left|\frac{d \phi}{d t}\right|=|8 t+6| \Rightarrow\left(\frac{d \phi}{d t}\right)_{t=2}=8 \times 2+6$ Induced emf in the coil $=22 \mathrm{~V}$

Hence, the correct answer is option: 'A'.

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