Question

Flux $\phi$ (in weber) in a closed circuit of resistance $10\,ohm$ varies with time $t$ (in sec) according to the equation $\phi=6t^{2}-5t+1.$ What is the magnitude of the induced current at $t=0.25\,s$ ?

• A. $1.2A$
• B. $0.8A$
• C. $0.6A$
• D. $0.2A$

Answer 1

Answer: (D)

By using $i=\frac{e}{R}=-\frac{1}{R}\frac{d \phi}{d t}$
$i=-\frac{1}{10}\frac{d}{d t}\left(6 t^{2} - 5 t + 1\right)=-\frac{1}{10}\left(\right.12t-5\left.\right)$
$i=-\frac{1}{10}\left(\right.12\times 0.25-5\left.\right)=0.2A$