What Occurs in the Differential Equation I = C*(dv/dt) as t Approaches Zero?

[Andrew123]

What happens in the differential equation: I = C*(dv/dt) when we limit t ---> 0 and what is the working? This isn't really a homework Q its just me wanting to know the theory behind this. TY in advance for looking and helping.

 

[Dick]

I(t) and V(t) are both functions of time if C is capacitance. This is just a relation between I and V. You can't 'solve' it unless you describe the physical situation.

 

[HallsofIvy]

What happens in the differential equation: I = C*(dv/dt) when we limit t ---> 0 and what is the working? This isn't really a homework Q its just me wanting to know the theory behind this. TY in advance for looking and helping.

It's not clear what you are saying. Take the limit of what as t goes to 0? Both sides of the equation? If so, are I and C constants or functions of t? If constants then dv/dt is a constant and so taking the limit as t goes to 0 doesn't change anything- you would still have I= C(dv/dt). If they are continuous functions of t, then taking the limit as t goes to 0 gives I(0)= C(0)(dv/dt) where dv/dt is now evaluated at t= 0.