Differentiation with electricity help

1. The problem statement, all variables and given/known data



A circuit consists of 230V supply, a switch, a 2mH inductor and a 12k ohm resistor in series





When the switch is closed at time t=o, a current i begins to flow in the circuit: The current is modelled by the following equation:





i= v/r (1-e^-Rt/L)





Determine the rate of change of the current at the following times:

i) t= o ns

ii) t= 1 ns

iii) t= 50 ns





I have subbed the values in and come up with answers of

i) i= 0 amps

ii) i= 1.146x10^-4 amps

iii) i= 4.968x10^-3 amps





But is this right? Do i need to insert the values in first and simplify the equation? Then differentiate it then sub in values for t?





Any help would be appreciated.



2. Relevant equations



i= v/r (1-e^-Rt/L)



3. The attempt at a solution



i= v/r (1-e^-Rt/L)

i= 230/12x10^3 (1-e^-12x10^3x50x10^-9/2x10^-3)

i= 0.0916 (0.25918)

i= 4.968x10^-3 amps