Flux - in weber in a closed circuit of resistance 10 - varies with time t in seconds according to the equation - - 6t2 - 5t - 1- What is the magnitude of the induced current at t - 0-25 s-

Induced emf in the loop is given by ϵ = dϕdt Induced current i=1R( dϕdt) =1R( ddt (6t^2 5t+1)) =110(5 12t) At t=0.25 s i=5 12× nbsp; 0.2510=5 310 =0.2 A ...

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Byju's Answer

Standard XI

Physics

Magnetic Flux and Faraday's Law

Flux ϕ in web...

Question

Flux $ϕ$ (in $w e b e r$ ) in a closed circuit of resistance $10 Ω$ varies with time $t$ (in $s e c o n d s$ ) 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

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0.2 A

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0.6 A

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0.8 A

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Solution

The correct option is B $0.2 A$

Induced emf in the loop is given by
$ϵ = - \frac{d ϕ}{d t}$
Induced current
$i = \frac{1}{R} (- \frac{d ϕ}{d t})$
$= \frac{1}{R} (- \frac{d}{d t} (6 t^{2} - 5 t + 1))$
$= \frac{1}{10} (5 - 12 t)$

At $t = 0.25 s$
$i = \frac{5 - 12 \times 0.25}{10} = \frac{5 - 3}{10}$
$= 0.2 A$

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

The correct option is B 0.2 A Induced emf in the loop is given by ϵ=−dϕdt Induced current i=1R(−dϕdt) =1R(−ddt(6t2−5t+1)) =110(5−12t) At t=0.25 s i=5−12×0.2510=5−310 =0.2 A

Flux $ϕ$ (in $w e b e r$ ) in a closed circuit of resistance $10 Ω$ varies with time $t$ (in $s e c o n d s$ ) according to the equation $ϕ = 6 t^{2} - 5 t + 1$ . What is the magnitude of the induced current at $t = 0.25 s$ ?