Differentiation with electricity help

[Thepiman]

Homework Statement

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 modeled 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.

Homework Equations

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

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

 

[STEMucator]

If I'm reading the question correctly, they want the 'rate of change' of the current at particular times. This means you would want to differentiate with respect to time first before plugging in your time values.