Q169 / 180 · COMEDK 2023 (Morning Shift) · 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
- A16 V
- B18 V
- Correct answerC22 V
- D40 V
Solution
The induced electromotive force (emf) in a coil is given by Faraday's law of induction, which states that the magnitude of the induced emf is equal to the rate of change of magnetic flux through the coil:
$|\varepsilon| = \left| \dfrac{d\phi}{dt} \right|$
Given the magnetic flux $\phi = 4t^2 + 6t + 9$, we differentiate this expression with respect to time $t$:
$\dfrac{d\phi}{dt} = \dfrac{d}{dt}(4t^2 + 6t + 9)$
$\dfrac{d\phi}{dt} = 8t + 6$
To find the induced emf at $t = 2$ s, we substitute $t = 2$ into the expression for the rate of change of flux:
$\varepsilon = 8(2) + 6$
$\varepsilon = 16 + 6 = 22 \text{ V}$
Answer: 22 V
$|\varepsilon| = \left| \dfrac{d\phi}{dt} \right|$
Given the magnetic flux $\phi = 4t^2 + 6t + 9$, we differentiate this expression with respect to time $t$:
$\dfrac{d\phi}{dt} = \dfrac{d}{dt}(4t^2 + 6t + 9)$
$\dfrac{d\phi}{dt} = 8t + 6$
To find the induced emf at $t = 2$ s, we substitute $t = 2$ into the expression for the rate of change of flux:
$\varepsilon = 8(2) + 6$
$\varepsilon = 16 + 6 = 22 \text{ V}$
Answer: 22 V
Hence, the correct answer is option: 'C'.