Question

The magnetic flux (in weber) in a closed circuit of resistance $20\ \Omega$ varies with time $t$ second according to equation $\phi = 5t^2 - 6t + 9$. The magnitude of induced current at $t = 0.2$ second is

• A. $0.8\text{ A}$
• B. $1\text{ A}$
• C. $0.2\text{ A}$
• D. $0.4\text{ A}$

Hint:

Always differentiate the equation before substituting the time value! Substituting $t=0.2$ into the flux equation first would turn it into a constant, which incorrectly makes its derivative zero.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
Magnetic flux φ = 5t² – 6t + 9 through a loop with R = 20 Ω; find induced current at t = 0.2 s.

Step 2: Key Formula or Approach:
Induced emf e = –dφ/dt. Current I = |e|/R.

Step 3: Detailed Explanation:
dφ/dt = 10t – 6. At t = 0.2: e = –(2 – 6) = 4 V. I = 4/20 = 0.2 A.

Step 4: Final Answer:
Induced current is 0.2 A, matching option (C).