Question

The differential equation for the current i in an electric circuit containing resistance R=250 ohm and an inductance of L=640 henery in series with an
electromotive force E=500 volts is​

Answer 1

Step-by-step explanation:

hope it will help you bro

Answer 2

Given:

        Resistance $(R) = 250$ ohm

        Inductance $(L) = 640$ henery

       Electromotive force $(E) = 500$ volts

    Differential equation is $E = Ri + L \frac{di}{dt}$

Separating the Variables and integrating gives,

      $\int^i_0 \frac{1}{E-iR} di =\int^t_0 \frac{1}{L} dt$

       $\frac{1}{R} ln (\frac{E}{E-iR} ) = \frac{t}{L}$

        $i = \frac{E}{R} (1 - e^-^R^\frac{t}{L} )$

        AS $t \longrightarrow \infty \Rightarrow e^-^R^t \longrightarrow 0$

            $i = t \longrightarrow \infty \Rightarrow e^-^R^t \longrightarrow 0$

        ∴    $i = \frac{500}{250} = 2 amp$