Question

The magnetic flux in a closed circuit, of resistance $20\Omega$, varies with time $\left(t\right)$ according to the equation $\varphi =7t^2-4t$. Where $\varphi$ is in $\text{webers}$ and $\text{t}$ is in $\text{seconds}$. The magnitude of the induced current at $t=0.25\text{sec}$ is,

• A. $0.25\text{A}$
• B. $0.025\text{A}$
• C. $50\text{mA}$
• D. $175\text{mA}$

Answer 1

The correct option is B $0.025\text{A}$

Given:

$\varphi =7t^2-4t$

$R=20\Omega$

$t=0.25\text{sec.}$

Magnitude of induced emf in circuit is,

$\left|\begin{array}{c}E\end{array}\right|=\left|\begin{array}{c}\frac{d\varphi }{dt}\end{array}\right|=\left|\begin{array}{c}\frac{d}{dt}(7t^2-4t)\end{array}\right|$

$\Rightarrow E=\left|\begin{array}{c}14t-4\end{array}\right|$

$\therefore$ Induced current will be,

$i=\frac{\left|\begin{array}{c}E\end{array}\right|}{R}=\frac{\left|\begin{array}{c}14t-4\end{array}\right|}{20}$

at $t=0.25\text{sec.}$

$i=\frac{\left|\begin{array}{c}14\times 0.25-4\end{array}\right|}{20}$

$i=\frac{0.5}{20}=2.5\times {10}^{-2}\text{A}$

Hence, option ($C$) is the correct answer.