What is the current when time = 2 seconds?

Question

The charge q on a certain capacitor in an amplifier circuit as a function of time t is given by:

 

just to be clear π= pie

 

q = e^-0.1t (0.2 sin 120πt + 0.8 cos 120πt)

 

the current i in the circuit is the instantaneous time rate of change of the charge. what is the current when time = 2 seconds?

Answer 1

Take the derivative of q, and you will get the current function. Then substitute t = 2 seconds in to the current function.

Note that q is a product of two functions of t. Therefore you should use the product rule when finding the derivative.