Question

magnetic flux through a closed conducting loop of resistance $0.4\Omega$ changes with time according to the equation $\Phi=0.20t^{2}+0.40t+0.60$ where $t$ is time in seconds. The heat produced from $t=0$ to $t=5$ sec is.

• A. $\frac{46}{3}J$
• B. $\frac{76}{3}J$
• C. $\frac{56}{3}J$
• D. $\frac{86}{3}J$

Answer 1

Answer: (D)

$\epsilon =-\frac{dϕ}{dt}=-\left(\right.0.4t+0.4\left.\right)$
$H=\displaystyle \int \frac{\epsilon ^{2}}{R}\cdot dt=\displaystyle \int _{0}^{5}\frac{\left[\right. 0 . 4 t + 0 . 4 \left]\right.^{2}}{R}\cdot dt=\frac{86}{3}J$