The magnetic flux linked with a coil satisfies the relation φ= (4t2 + 6t + 9) Wb, where t is the time in second. The e.m.f. induced in the coil at t = 2 second is

Question

The magnetic flux linked with a coil satisfies the relation φ= (4t2 + 6t + 9) Wb, where t is the time in second. The e.m.f. induced in the coil at t = 2 second is (A) 22 V (B) 18 V (C) 16 V (D) 40 V

Tardigrade Admin · Accepted Answer

Given φ=4 t2+6 t+9 and t=2 s We know that ε=(d φ/d t) Here, (d φ/d t)=8 t+6 ((d φ/d t))t=2 =8 × 2+6 ε =22 V

Q. The magnetic flux linked with a coil satisfies the relation $ϕ = (4 t^{2} + 6 t + 9) Wb$ , where $t$ is the time in second. The e.m.f. induced in the coil at $t = 2$ second is

22 V

18 V

16 V

40 V

Given $ϕ = 4 t^{2} + 6 t + 9$ and $t = 2 s$
We know that $ε = \frac{d ϕ}{d t}$
Here, $\frac{d ϕ}{d t} = 8 t + 6$
$(\frac{d ϕ}{d t})_{t = 2} = 8 \times 2 + 6$
$ε = 22 V$

Q. The magnetic flux linked with a coil satisfies the relation ϕ=(4t2+6t+9)Wb, where t is the time in second. The e.m.f. induced in the coil at t=2 second is