Magnetic flux (in weber) in a closed circuit of resistance 20Ω...

Given that magnetic flux $ϕ = 8{t}^{2} - 9t + 5$

According to Faraday's law of electromagnetic induction

$emf = - \dfrac{dϕ}{dt} = - \left(16t - 9\right)$

At $t = 0 . 25s$

$emf = - \left[\left(16 \times 0 . 25\right) - 9\right] = 5V$

Current $= \dfrac{emf}{Resistance} = \dfrac{5V}{20Ω}$

$= \dfrac{1}{4}A = \dfrac{1000}{4}mA = 250mA$