Q179 / 180 · COMEDK 2024 (Evening Shift) · Physics
The magnetic flux linked with a coil is given by the equation: $\phi = 8t^2 + t + 10$. The e.m.f. induced in the coil at $t = 3$ seconds will be:
- Correct answerA49 V
- B16 V
- C33 V
- D20 V
Solution
The magnetic flux linked with the coil is given by $\phi = 8t^2 + t + 10$.
The induced electromotive force (e.m.f.) in the coil is given by Faraday's law of induction: $\varepsilon = -\dfrac{d\phi}{dt}$.
Differentiating the flux with respect to time $t$:
$\dfrac{d\phi}{dt} = \dfrac{d}{dt}(8t^2 + t + 10) = 16t + 1$.
The magnitude of the induced e.m.f. is $|\varepsilon| = |-(16t + 1)| = 16t + 1$.
The e.m.f. induced in the $3^{\text{rd}}$ second refers to the instantaneous e.m.f. at $t = 3$ s.
Substituting $t = 3$ into the expression for the magnitude of the e.m.f.:
$|\varepsilon| = 16(3) + 1 = 48 + 1 = 49$ V.
Answer: 49 V
The induced electromotive force (e.m.f.) in the coil is given by Faraday's law of induction: $\varepsilon = -\dfrac{d\phi}{dt}$.
Differentiating the flux with respect to time $t$:
$\dfrac{d\phi}{dt} = \dfrac{d}{dt}(8t^2 + t + 10) = 16t + 1$.
The magnitude of the induced e.m.f. is $|\varepsilon| = |-(16t + 1)| = 16t + 1$.
The e.m.f. induced in the $3^{\text{rd}}$ second refers to the instantaneous e.m.f. at $t = 3$ s.
Substituting $t = 3$ into the expression for the magnitude of the e.m.f.:
$|\varepsilon| = 16(3) + 1 = 48 + 1 = 49$ V.
Answer: 49 V
Hence, the correct answer is option: 'A'.