Question

Magnetic flux linked with the coil in weber is given by the equation \(\Phi = 5t^2+6t+11\). The e.m.f. induced in the coil in the \(5^{\text{th}}\) second will be

• A. \(10\) V
• B. \(51\) V
• C. \(102\) V
• D. \(166\) V

Hint:

The e.m.f. in the 5th second is the average rate of change of flux between t = 4 s and t = 5 s.

Answer 1

The Correct Option is B

Step 1: Interval:
"In the 5th second" means the interval $4\leq t\leq5$.

Step 2: Use the Mean Slope:
The rate of change of $5t^2+6t+11$ is $10t+6$. Its value at the middle of the interval, $t=4.5$ s, is $51$. This equals the average rate over the interval because the rate is linear in $t$.

Step 3: Answer:
The e.m.f. is 51 V in magnitude. Option (B).

Final Answer:
Option (B). \[ \boxed{\text{(B) } 51\ \text{V}} \]