Flux (φ) (in weber) in a closed circuit of resistance 20 Ω varies with time t (in second) according to equation φ=6 t2-5 t+1. The magnitude of the induced current at t=0.25 s, is

Question

Flux (φ) (in weber) in a closed circuit of resistance 20 Ω varies with time t (in second) according to equation φ=6 t2-5 t+1. The magnitude of the induced current at t=0.25 s, is (A) 1.2 A (B) 0.8 A (C) 0.6 A (D) 0.1 A

Tardigrade Admin · Accepted Answer

From Faraday's second law, e=-(d φB/d t) =-(d/d t)(6 t2-5 t+1)=-(12 t-5) At t=0.25 s =-[12 ×(0.25)-5]=+2 V Now, i=(e/R)=(2/20)=0.1 A

Q. Flux $(ϕ)$ (in weber) in a closed circuit of resistance $20 Ω$ varies with time $t$ (in second) according to equation $ϕ = 6 t^{2} - 5 t + 1$ . The magnitude of the induced current at $t = 0.25 s$ , is

$1.2 A$

$0.8 A$

$0.6 A$

$0.1 A$

From Faraday's second law, $e = - \frac{d ϕ _{B}}{d t}$
$= - \frac{d}{d t} (6 t^{2} - 5 t + 1) = - (12 t - 5)$
At $t = 0.25 s = - [12 \times (0.25) - 5] = + 2 V$
Now, $i = \frac{e}{R} = \frac{2}{20} = 0.1 A$

Q. Flux (ϕ) (in weber) in a closed circuit of resistance 20Ω varies with time t (in second) according to equation ϕ=6t2−5t+1. The magnitude of the induced current at t=0.25s, is

1.2A

0.8A

0.6A

0.1A