Final answer:
The steady state current in the circuit can be found by solving the given differential equation and differentiating the charge function with respect to time. To find the current at t = 3.00 s, you substitute that time into the solved current equation. For a capacitor with a sinusoidal charge function, the current is the negative of the derivative of the charge function with respect to time.
Step-by-step explanation:
To find the steady state current in a circuit described by the differential equation 1/10 Q''+2 Q'+100 Q=3 cos 50 t-6 sin 50 t, we need to consider the forced response of the circuit due to the sinusoidal driving functions. The steady state current corresponds to the current that flows in the circuit long after any transients have died out, which is typically found by solving the differential equation for the particular solution. However, since current i(t) is the time derivative of charge Q(t), we can find the current by differentiating the charge equation provided.
To find the current at a specific time, such as t = 3.00 s, we would substitute that time value into the solved current equation. The specific relationship between charge and current in a circuit with a sinusoidal source is that the current can be found by differentiating the charge function with respect to time, which gives us i(t) = dQ(t)/dt. In the case of the charge on a capacitor being modeled by Q(t) = Qmax cos (wt + π), the current as a function of time would be i(t) = -wQmax sin (wt + π).