Help! I am having trouble trying to compute the inductor current changes in a parallel R (1Kohms), and L (1mH). They are being driven by a current source of 1A. How do I verify that the current flows in the inductor changes by 63% of its initial value in one time constant.Also, How to,1. Analytical derivation of voltage and current across L2. How the specific values of R and L affect the transient behavior of voltage and current across the inductor3. Compare the analytical solution with the numeric results (I used LT SPICE to successfully obtain the voltage and current waveform across R and L)any help on any of the questions, particularly, the 63% question and Q1 and Q2 would be greatly appreciated. Thanks.
If the norton equivalent is a 1amp current source in shunt with a 1k, the thevenin equivalent is 1kV in series with 1k. So you can also solve this assuming that you have a 1kV in series with 1k and in series with L of 1mH, returning to negative of 1kV. the results will be same.
For this circuit, the current of the source is equal to the current through the resistor plus the inductor current. Therefore Ise/R+(1/L)integral(e dt), where e is the voltage across the current source. I'm not into solving equations like this any more, but the solution will be something like eI R e^-t/T where TL/R. e^-1.368 and 1-.36863.2%.
This problem is easy to solve using LaPlace transforms For the circuit indicated; The time constan, tc L/R In s domain; Solving for inductor current, Convert R and I to thevenin equivalent, a voltage source I*R in series with R Ohms. IL(s) (I*R)/[s*(R + s*L)] Transforming to the time domain; IL(t) I(1 - exp[(R/L)*t] IL(t) I(1 - exp[(1/tc)*t] at one time constant t tc t L/R Then, IL(t) I{1 - exp[1]} IL(t) I(1 - 0.367879) IL(t) I(0.632121) IL reaches 63.2% of maximum in 1 time constant Solving for volatge across the inductor, VL(s) I*R/(s + R/L) then; VL(t) I*R*exp[(R/L)*t] VL(t) I*R*exp[t/(tc)]
