Question

The magnetic flux across a loop of resistance $10\Omega$ is given by $ɸ=5t^2–4t+1$ weber. How much current is induced in the loop after $0.2$sec?

• A. $0.4A$
• B. $0.2A$
• C. $0.04A$
• D. $0.02A$

Answer 1

The correct option is B

$0.2A$

Solution:

Step1: Given data:

$ɸ=5t^2–4t+1$

The magnetic flux across a loop of resistance$\left(R\right)=10\Omega$

The time $\left(t\right)=0.2sec$

Step 2: Formula used and differentiate:

$\begin{array}{rcl}ɸ& =& 5t^2–4t+1\\ Emf,e& =& -\frac{d\varphi }{dt}\\ e& =& -\left(10t-4\right)\end{array}$

Use the current induced in the loop $i=\frac{e}{R}$

Now substitute the value in the formula,

$$\begin{gathered} i=-\frac{\left(10t-4\right)}{10}(att=0.2sec) \\ i=-\frac{\left(10\times 0.2-4\right)}{10} \\ i=\frac{2}{10} \\ i=0.2A \end{gathered}$$

Therefore the current $0.2A$is induced in the loop after $0.2$sec.

Hence, the correct option is B.