Question

If the magnetic flux through a coil at any time $ t $ is given by $ \phi=(4t^{2}+5t-3) $ , then the increase in induced emf (in volt) $ 2 $ second after $ t = 0 $ is

• A. $ 5 $
• B. $ 16 $
• C. $ 21 $
• D. zero

Answer 1

Answer: (B)

As $\phi=4t^{2}+5t-3$
$\therefore $ The induced emf in the coil is
$\varepsilon=\frac{d \phi}{dt}$ (in magnitude)
$=\frac{d}{dt}\left(4t^{2}+5t+3\right)=8t+5V$
At $t=0, \varepsilon_{1}=5V$ and at $t=2\,s, \varepsilon_{2}=21\,V$
$\therefore $ The increase in induced emf is
$\Delta\varepsilon=\varepsilon_{2}-\varepsilon_{1}=21\,V-5V$
$=16 V$