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The normal magnetic flux passing through a coil changes with time according to the equation $\phi=6 t^{2}-5 t+1$. What is the magnitude of the induced current at $t=0.253 \mathrm{~s}$ and resistance $10 \Omega$ ?
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The correct answer is:
$0.2 \mathrm{~A}$
Given, magnetic flux
$$
\phi=6 t^{2}-5 t+1, R=10 \Omega
$$
Induced emf,
$e=-\frac{d \phi}{d t}$
$=-\frac{d}{d t}\left(6 t^{2}-5 t+1\right)$
$e=-12 t+5$
At $t=0.253 \mathrm{~s}, e=-12 \times 0.253+5$
$=-3.036+5=1.964 \mathrm{~V}$
$\therefore$ Induced current, $I=\frac{e}{R}$
$=\frac{1.964}{10}=0.1964 \mathrm{~A} \simeq 0.2 \mathrm{~A}$
$$
\phi=6 t^{2}-5 t+1, R=10 \Omega
$$
Induced emf,
$e=-\frac{d \phi}{d t}$
$=-\frac{d}{d t}\left(6 t^{2}-5 t+1\right)$
$e=-12 t+5$
At $t=0.253 \mathrm{~s}, e=-12 \times 0.253+5$
$=-3.036+5=1.964 \mathrm{~V}$
$\therefore$ Induced current, $I=\frac{e}{R}$
$=\frac{1.964}{10}=0.1964 \mathrm{~A} \simeq 0.2 \mathrm{~A}$
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