How about a response Ex?
Before going further, I would like to understand what is your goal. Is it to affirm that, when a constant voltage is abruptly applied to a solenoid, there is an induced emf whose the mean voltage is a not null DC? The equation is simple: L*di/dt + R*i(t) = V * h(t) L is the inductance, R its resistance, V the voltage and h(t) the Heaviside step function h(t)=0 for t<0 and h(t)=1 for t>=0. Just before t=0, i=0. Just after: L*di/dt + R*i(t) = V whose the solution for i is well known: i = V/R * (1  e ^{t/τ}) where τ= R/L L/R Only the variation of i produces emf. If we suppose a perfect coupling with the solenoid: emf = k * di/dt. di/dt =d/dt (V/R * (1  e ^{t/τ})) = V/R * d/dt ( e ^{t/τ}) = V/R * 1/τ * e ^{t/τ} = V/L * e ^{t/τ}As e ^{t/τ} is always >0, so is di/dt and emf. Your goal is correct. I must admit that my affirmation pretending the contrary made an implicit assumption that I should have given: it is true only when the initial and final conditions are the same (for example i=0, or i=anything but the signal is periodic) which was not the case here. Do you agree? I just still ask me a final question about the t<0 to t=0 transition, as modelized in the equation. Is it physical? I think it is but I have some doubt.
« Last Edit: 20120511, 16:14:55 by exnihiloest »
