The magnetic flux in a closed circuit of resistance 10 Ω varies with time as φ= (2 t-4 t^2+1 ) . The current in the loop will change its direction after a time of

Correct answer: (A) 0.25 sec. e =-(d φ)/dt=[-2+8 t+0] ⇒ 8 t=2 ⇒ t=1/4 sec=0.25 sec

Q111 / 120 · VITEEE 2016 · Physics

The magnetic flux in a closed circuit of resistance $10 \Omega$ varies with time as $\phi=\left(2 \mathrm{t}-4 \mathrm{t}^{2}+1\right)$. The current in the loop will change its direction after a time of

Correct answer
A
$0.25 \mathrm{sec}$
B
$0.5 \mathrm{sec}$
C
$1 \mathrm{sec}$
D
none

Solution

$\begin{aligned} \mathrm{e} &=-\frac{\mathrm{d} \phi}{\mathrm{dt}}=[-2+8 \mathrm{t}+0] \\ & \Rightarrow 8 \mathrm{t}=2 \Rightarrow \mathrm{t}=\frac{1}{4} \mathrm{sec}=0.25 \mathrm{sec} \end{aligned}$

Hence, the correct answer is option: 'A'.

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