H
[email protected]
- Jan 1, 1970
- 0
Hi!
Could you possibly give me a physical interpretation of the homogeneous
solution of the differential equation describing a series RL circuit
powered by a sinusoidal source?
The equation that describes the circuit is:
Vo*sin(wt)-L*d/dt(i(t)) = i(t)*R
The solution (using i(0)=0 as initial condition):
i(t)= transient_response + steady_state_response
(or homogeneous + (particular or inhomogeneous))
where
transient_response = [Vo * wL / (R^2+(wL)^2)] * exp(-R/L*t)
steady_state_response = Vo / (sqrt(R^2+(wL)^2)) * sin(w*t-arctan(wL/R))
using also:
a * sin(wt) + b * cos (wt) = 1/sqrt(a*a+b*b) * sin(wt + arctan (b/a))
What is the physical interpretation of the transient response?
Thank you in advance,
Hugo.
Could you possibly give me a physical interpretation of the homogeneous
solution of the differential equation describing a series RL circuit
powered by a sinusoidal source?
The equation that describes the circuit is:
Vo*sin(wt)-L*d/dt(i(t)) = i(t)*R
The solution (using i(0)=0 as initial condition):
i(t)= transient_response + steady_state_response
(or homogeneous + (particular or inhomogeneous))
where
transient_response = [Vo * wL / (R^2+(wL)^2)] * exp(-R/L*t)
steady_state_response = Vo / (sqrt(R^2+(wL)^2)) * sin(w*t-arctan(wL/R))
using also:
a * sin(wt) + b * cos (wt) = 1/sqrt(a*a+b*b) * sin(wt + arctan (b/a))
What is the physical interpretation of the transient response?
Thank you in advance,
Hugo.