Question

The magnetic flux linked with a loop changes with time according to the equation, $\varphi =a{t}^2+bt+c$ where $t$ is time in $\text{s}$ and $a,b$ and $c$ are constants. The SI unit of $a$ is

• A. $\text{V}$
• B. $\frac{\text{V}}{\text{s}}$
• C. $\text{V - s}$
• D. $\text{Wb}$

Answer 1

The correct option is B $\frac{\text{V}}{\text{s}}$

Given:

$\varphi =a{t}^2+bt+c$

According to Faraday's law of electromagnetic induction, magnitude of induced emf,

$E=\frac{d\varphi }{dt}$

$=\frac{d}{dt}(a{t}^2+bt+c)=2at+b$

$\therefore \left[E\right]=\left[at\right]$

$\Rightarrow \left[a\right]=\left[\frac{E}{t}\right]$

$\Rightarrow \left[a\right]=\left[\frac{\text{V}}{\text{s}}\right]$

Hence, option $\left(B\right)$ is the correct answer.