Engineering Current through inductor in a circuit with a sinusoidal voltage source

[AbbeAbyss]

Homework Statement

http://www.wifstrand.se/Albert/stuff/p7.7-1.png

Homework Equations

v_L = L * (di_L / dt).

All of the inductors can be reduced to a single 8 H inductor, so

i_L = (6 / 8) * ∫ cos 100t dt = 0.0075 sin 100t

if you integrate from 0 to t.

The Attempt at a Solution

The formula states that i_L = i_L(t₀) + ∫ v_L dt if you integrate from some initial condition current t₀ to t. I get the correct answer if I integrate from 0 to t, but I fail to see what i_L(t₀) is and how we can use 0 for the lower bound.

It seems as if we can just assume that t₀ = 0 and that i_L(t₀) = 0, if so, why is that?

 

[rude man]

Homework Statement

http://www.wifstrand.se/Albert/stuff/p7.7-1.png

Homework Equations

v_L = L * (di_L / dt).

All of the inductors can be reduced to a single 8 H inductor, so

i_L = (6 / 8) * ∫ cos 100t dt = 0.0075 sin 100t

if you integrate from 0 to t.

The Attempt at a Solution

The formula states that i_L = i_L(t₀) + ∫ v_L dt if you integrate from some initial condition current t₀ to t. I get the correct answer if I integrate from 0 to t, but I fail to see what i_L(t₀) is and how we can use 0 for the lower bound.

It seems as if we can just assume that t₀ = 0 and that i_L(t₀) = 0, if so, why is that?

You have di/dt = V/L so
i = ∫(V/L)dt + constant (indefinite integral + a constant)

To evaluate the constant, asume V = 0 for t < 0. Then, at t = 0, a sudden voltage V = 6V is applied to L. What is the current then at t = 0? What is the constant? Do you see now why your last statement is correct?

 

[AbbeAbyss]

You have di/dt = V/L so
i = ∫(V/L)dt + constant (indefinite integral + a constant)

To evaluate the constant, asume V = 0 for t < 0. Then, at t = 0, a sudden voltage V = 6V is applied to L. What is the current then at t = 0? What is the constant? Do you see now why your last statement is correct?

Yes, I see now that at t = 0 (or rather t = 0⁺ denoting the exact moment the voltage 6 * cos 0 is applied) the current is 0 since the current through an inductor can't change instantaneously, thanks.