ECET 305 digital signal processing class week two Discussion questions

1.For RL series circuit, R = 4Ω and L = 0.5 H. The source voltage V = 12 Vdc is applied. Find the current i(t) using the Laplace transform. Assume all initial conditions are zeros. 

a) First, write the voltage equation in terms of a differential equation. 
b) Second, apply the Laplace transform on the equation. For example, if you take the Laplace transform on V = 12 V, then the Laplace transform of 12 = 12/s,  the Laplace transform of i(t) =I(s) etc. 
c)  Rearrange the transformed equation for the current I(s). 
d) Take the inverse Laplace transform of I(s) to find the current i(t). 
e) The answer should be i(t) = 3(1-e^(-8t)). 
f) From the answer (e), what is the transient and the final (stable or steady-state) value? Describe i(t) from (e) more specifically. 
g) What is the time constant of the circuit? Calculate it.