The normal magnetic flux passing through a coil changes with time according to the equation φ = 6t2 - 5t + 1. What is the magnitude of the induced current at t = 0.253 s and resistance 10 Ω ?

Question

The normal magnetic flux passing through a coil changes with time according to the equation φ = 6t2 - 5t + 1. What is the magnitude of the induced current at t = 0.253 s and resistance 10 Ω ? (A) 1.2 A (B) 0.8 A (C) 0.6 A (D) 0.2 A

Tardigrade Admin · Accepted Answer

Here , Magnetic flux, φ = 6t2 - 5t + 1 Resistance, R = 10 Ω The induced emf is ε = - (dφ/dt) = - (d/dt) (6t2 - 5t+ 1)=-(12t - 5 ) At t = 0.253 s ε = -(12 × 0.253 - 5 ) = 1.964 V = 2 V ∴ Induced current, I = ( ε/R) = (2/10) = 0.2 A

Q. The normal magnetic flux passing through a coil changes with time according to the equation $ϕ = 6 t^{2} - 5 t + 1$ . What is the magnitude of the induced current at $t = 0.253 s$ and resistance $10 Ω$ ?

1.2 A

0.8 A

0.6 A

0.2 A

Here ,
Magnetic flux, $ϕ = 6 t^{2} - 5 t + 1$
Resistance, $R = 10 Ω$
The induced emf is
$ε = - \frac{d ϕ}{d t} = - \frac{d}{d t} (6 t^{2} - 5 t + 1) = - (12 t - 5)$
At $t = 0.253 s$
$ε = - (12 \times 0.253 - 5) = 1.964 V = 2 V$
$∴$ Induced current, $I = \frac{ε}{R} = \frac{2}{10} = 0.2 A$

Q. The normal magnetic flux passing through a coil changes with time according to the equation ϕ=6t2−5t+1. What is the magnitude of the induced current at t=0.253s and resistance 10Ω ?