Question

A coil of resistance $400\Omega$ is placed in magnetic field. If the magnetic flux ' $\phi$ ( Wb ) linked with the coil varies with time ' $t$ ( s ) is $\phi = 50t^2 + 4$, the current in the coil at $t = 2\text{ s}$ will be}

• A. 1 A
• B. 2 A
• C. 0.5 A
• D. 0.1 A

Hint:

In induction problems: \[ \mathcal{E}=\left|\frac{d\phi}{dt}\right| \] Differentiate first, then divide by resistance to get current.

Answer 1

The Correct Option is C

Concept:
Induced emf is: \[ \mathcal{E}=\left|\frac{d\phi}{dt}\right| \] Current in the coil is: \[ I=\frac{\mathcal{E}}{R} \] ip

Step 1: Differentiate the flux function.
Given: \[ \phi=50t^2+4 \] So, \[ \frac{d\phi}{dt}=100t \] ip

Step 2: Find emf at \(t=2\text{ s}\).
\[ \mathcal{E}=100\times 2=200\text{ V} \] ip

Step 3: Find current in the coil.
\[ I=\frac{200}{400}=0.5\text{ A} \] ip Hence, the correct answer is:
\[ \boxed{(C)\ 0.5\text{ A}} \]