Question

The magnetic flux through each turn of a coil having 200 turns is given as $(t^2-2t)\times {10}^{-3}Wb$, where t is in second. The emf induced in the coil at t = 3 s is

• A. 0.7 V
• B. 1.2 V
• C. 0.8 V
• D. 0.9 V

Answer 1

The correct option is C 0.8 V

According to Faraday's law , the induced emf in a coil (having N turns) is the rate of change of magnetic flux linked with coil ,

$e=N\frac{d{\varphi }_B}{dt}$

given - ${\varphi }_B=(t^2-2t)\times {10}^{-3}$

or $\frac{d{\varphi }_B}{dt}=(2t-2)\times {10}^{-3}$

Therefore , induced emf in coil , having turns $N=200$ ,

$e=200(2t-2)\times {10}^{-3}$

at $t=3s$

$e=200(2\times 3-2)\times {10}^{-3}=0.8V$