Suppose the emf of the battery in following circuit varies w

Suppose the emf of the battery in following circuit varies with time t so that the current is given by i(t) =3.0 +5.0t, where i is in amperes and t is in seconds. If R =4.0 ohm and L = 6.0 H, and find an expression for the battery emf as a function of t.

Solution

in accordance with Kirchhoff\' law we have in the considered circuit two electromotive forces E and -Ldi/dt and so
E-Ldi/dt=iR
di/dt=5
E=(5+5t)x4+6x5 (1)

E= 20t+50