Question

Magnetic flux passing through a coil is initially $4\times {10}^{-4}\mathrm{W}\mathrm{b}$ . It reduces to $10\%$ of its original value in $t^{}$ second. If the emf induced is 0.72 mV then $t^{}$ in second is

• A. $0.3$
• B. $0.4$
• C. $0.5$
• D. $0.6$

Answer 1

Answer: (C)

${\varphi }_1=4\times {10}^{-4} \mathrm{Wb}$
${\varphi }_2=0.1\times {\varphi }_1=4\times {10}^{-5}\mathrm{ }\mathrm{Wb}$
$\epsilon =0.72\mathrm{m}\mathrm{V}$
$\therefore t=?$
Using $\epsilon =-\frac{d\varphi }{dt}\Rightarrow dt\Rightarrow \frac{d\varphi }{\epsilon }$
$=\frac{4\times {10}^{-4}-4\times {10}^{-5}}{72\times {10}^{-5}}=\frac{4\times {10}^{-5}\left(9\right)}{72\times {10}^{-5}}=\frac{1}{2}=0.5 \mathrm{ s}$