Question

The flux linked with the coil at any instant ' t ' is given by \( \phi = 12t^2 - 60t + 275 \). The magnitude of induced e.m.f. at \( t = 3 \text{ second} \) is

• A. $200 \text{ V}$
• B. $108 \text{ V}$
• C. $72 \text{ V}$
• D. $12 \text{ V}$

Hint:

- $\mathcal{E} = \left| \frac{d\phi}{dt} \right|$ - Differentiate first, then substitute value

Answer 1

The Correct Option is D

Concept: Induced emf: \[ \mathcal{E} = \left| \frac{d\phi}{dt} \right| \]

Step 1: Differentiate flux.
\[ \frac{d\phi}{dt} = 24t - 60 \]

Step 2: Substitute $t = 3$.
\[ \frac{d\phi}{dt} = 24(3) - 60 = 72 - 60 = 12 \]

Step 3: Take magnitude.
\[ \mathcal{E} = 12\ \text{V} \]