magnetic flux through a closed conducting loop of resistance 0.4Ω changes with time according to the equation Φ=0.20t2+0.40t+0.60 where t is time in seconds. The heat produced from t=0 to t=5 sec is.

Question

magnetic flux through a closed conducting loop of resistance 0.4Ω changes with time according to the equation Φ=0.20t2+0.40t+0.60 where t is time in seconds. The heat produced from t=0 to t=5 sec is. (A) (46/3)J (B) (76/3)J (C) (56/3)J (D) (86/3)J

Tardigrade Admin · Accepted Answer

ϵ =-(dÏ/dt)=-(.0.4t+0.4.) H= displaystyle ∫ (ϵ 2/R)⋅ dt= displaystyle ∫ 05([. 0 . 4 t + 0 . 4 ].2/R)⋅ dt=(86/3)J

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

$\frac{46}{3} J$

$\frac{76}{3} J$

$\frac{56}{3} J$

$\frac{86}{3} J$

$ϵ = - \frac{d ϕ}{d t} = - (0.4 t + 0.4)$
$H = \int \frac{ϵ ^{2}}{R} \cdot d t = \int_{0}^{5} \frac{[ 0.4 t + 0.4 ] ^{2}}{R} \cdot d t = \frac{86}{3} J$

Q. magnetic flux through a closed conducting loop of resistance 0.4Ω changes with time according to the equation Φ=0.20t2+0.40t+0.60 where t is time in seconds. The heat produced from t=0 to t=5 sec is.

346​J

376​J

356​J

386​J