(Solved): A simple electrical circuit consists of a constant resistance, \( R \), a constant inductance and ...

A simple electrical circuit consists of a constant resistance, \( R \), a constant inductance and an electromotive force, \( E(t) \). According to Kirchoff's second law, the current, \( i \), in the circuit satisfies the equation \( L \frac{d i}{d t}+R i=E(t) \). Solve the differential equation with the following condition: \( E(t)=E_{0} \) is a constant, and \( i=i_{0} \) when \( t=0 \). Determine the current, \( i \) when \( t \rightarrow \infty \). [10 marks]