Flux φ (in weber) in a closed circuit of resistance 10 ohm varies with time t (in sec) according to the equation φ=6t2-5t+1. What is the magnitude of the induced current at t=0.25 s ?

Question

Flux φ (in weber) in a closed circuit of resistance 10 ohm varies with time t (in sec) according to the equation φ=6t2-5t+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

Tardigrade Admin · Accepted Answer

By using i=(e/R)=-(1/R)(d φ/d t) i=-(1/10)(d/d t)(6 t2 - 5 t + 1)=-(1/10)(.12t-5.) i=-(1/10)(.12× 0.25-5.)=0.2A

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

$1.2 A$

$0.8 A$

$0.6 A$

$0.2 A$

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

Q. Flux ϕ (in weber) in a closed circuit of resistance 10ohm varies with time t (in sec) according to the equation ϕ=6t2−5t+1. What is the magnitude of the induced current at t=0.25s ?

1.2A

0.8A

0.6A

0.2A