JEE Main 2022 · 26 June · morning · Single correct · +4 / −1
The magnetic flux through a coil perpendicular to its plane is varying according to the relation φ = (5t³ + 4t² + 2t - 5) Weber. If the resistance of the coil is 5 ohm, then the induced current through the coil at t = 2 s will be,
- (a) 15.6 A
- (b) 16.6 A
- (c) 17.6 A
- (d) 18.6 A
Answer and solution
Answer (a) 15.6 A
Solution
Physics sir · 4 steps
The current comes from how fast the flux changes, so differentiate φ first and only then put in t = 2.
- Faraday's law. The induced emf equals the rate of change of flux, |e| = dφ/dt. The constant -5 does not change with time, so it drops out.
dφ/dt = 15t² + 8t + 2
- Emf at 2 s. At t = 2 s: 15 × 4 + 8 × 2 + 2 = 60 + 16 + 2 = 78 V.
- Ohm's law. I = e/R = 78/5 = 15.6 A.
- So. The induced current at t = 2 s is 15.6 A, option (a).
The idea to keep. Induced emf depends on the rate of change of flux, not on the flux itself. Differentiate first, then put in the time, then divide by R for the current.
Answer from the NTA final answer key. Solution by PrepWiser.