Electrical Circuit Analysis:

Given Circuit:
- The given electrical circuit is described by the differential equation L(di/dt) + iR = Ecos(ωt) with initial condition i(0) = 0.

Solving the Circuit:
1. First, we need to solve the given differential equation to find the current i(t) flowing through the circuit.
2. Rearranging the equation, we get L(di/dt) = -iR + Ecos(ωt).
3. Taking the Laplace transform of both sides, we get L(sI(s) - i(0)) = -IRI(s) + E/(s^2 + ω^2).
4. Substituting the initial condition i(0) = 0, we get LsI(s) = -IRI(s) + E/(s^2 + ω^2).
5. Solving for I(s), we get I(s) = E/(s(Ls + R) + ω^2).
6. Finally, taking the inverse Laplace transform of I(s), we get the current i(t) flowing through the circuit.

Explanation:
- By solving the differential equation and applying Laplace transforms, we can determine the current flowing through the given electrical circuit.
- The initial condition i(0) = 0 is considered in the calculation to find the complete solution for the current in the circuit.