AboutAlon Mandes Expertise Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems.
Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .
Experience 1. I'm a team member of mathnerds (math site for answering questions)
2. I'm a team member in the Student's Union of the Technion, helping
students who have problems in mathematics.
3. 2 years of experience as a math teacher in college.
4. I give free homework help for high school students in
Mathematics & Physics.
5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" ,
"Complex Functions".
Question Hi, Alon, I have the equation for the instantaneous voltage during the charge of a capacitor, viz v=V(1-e^t/T)where I know the all values in the right hand side. But why would this be a calculus problem? Is it because there is a constant in it? Should I differentiate the e? Kind regards, Mike
Answer The calculus term in this section is due to the nature of the
process of charging & discharging of the the electrical charge in
the capacitor.
Charging process:
----------------
Vs=Vc+Vr
Vs=Vc+ir
Vs=Vc+(dq/dt)r
Vs=Vc+(dVc/dt)rc
Vs=Vc+ζVc'
This is 1st order ODE , with solution of :
Vc(t)=Vs(1-e^[t/ζ]).
Discharging process:
-------------------
Vc+Vr=0
Vc+ir=0
Vc+ζVc'=0
The solution is :
Vc(t)=Vs*e^[-t/ζ]
Where Vs is determined via initial conditions of the capacitor.
