The differential equation I = C*(dv/dt) describes the relationship between current (I), capacitance (C), and the rate of change of voltage (dv/dt). As time (t) approaches zero, if I and C are treated as constants, the equation remains unchanged, resulting in I = C(dv/dt). However, if I and C are functions of time, the limit leads to I(0) = C(0)(dv/dt) evaluated at t = 0, indicating the need for specific initial conditions to fully understand the behavior of the system.
PREREQUISITESStudents of electrical engineering, physicists, and anyone interested in the theoretical aspects of circuit analysis and differential equations.
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.Andrew123 said: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.