A coil of resistance 400 Ω is placed in a magnetic field. If the magnetic flux φ (Wb) linked with the coil varies with time t(sec) as φ=50 t2+4. The current in the coil at t = 2 sec is

Question

A coil of resistance 400 Ω is placed in a magnetic field. If the magnetic flux φ (Wb) linked with the coil varies with time t(sec) as φ=50 t2+4. The current in the coil at t = 2 sec is (A) 0.5 A (B) 0.1 A (C) 2 A (D) 1 A

Tardigrade Admin · Accepted Answer

Here, φ=50 t2+4 W b, R=400 Ω Induced emf, ε=-(d φ/d t) =-(d/d t)(50 t2+4)=-100 t V At t=2 s, ε=-200 V |ε|=200 V Induced current in the coil at t=2 s is I=(|ε|/R)=(200 V/400 Ω)=(1/2) A=0.5 A

Q. A coil of resistance $400 Ω$ is placed in a magnetic field. If the magnetic flux $ϕ (Wb)$ linked with the coil varies with time t(sec) as $ϕ = 50 t^{2} + 4$ . The current in the coil at $t = 2 sec$ is

0.5 A

0.1 A

$2 A$

$1 A$

Here, $ϕ = 50 t^{2} + 4 Wb, R = 400 Ω$
Induced emf, $ε = - \frac{d ϕ}{d t}$
$= - \frac{d}{d t} (50 t^{2} + 4) = - 100 t V$
At $t = 2 s, ε = - 200 V$
$∣ ε ∣ = 200 V$
Induced current in the coil at $t = 2 s$ is
$I = \frac{∣ ε ∣}{R} = \frac{200 V}{400Ω} = \frac{1}{2} A = 0.5 A$

Q. A coil of resistance 400Ω is placed in a magnetic field. If the magnetic flux ϕ(Wb) linked with the coil varies with time t(sec) as ϕ=50t2+4. The current in the coil at t=2sec is