Final answer:
To determine the current in the RC circuit, differentiate the equation q(t) = Qe^(-t/RC) with respect to time. Substitute the given values and calculate the time constant. Then differentiate q(t) with respect to time to find the current.
Step-by-step explanation:
The current in an RC circuit can be determined using the equation I = dQ/dt, where I is the current and Q is the charge on the capacitor. Since we know that q(0) = 1 C, we can calculate the current by differentiating the equation q(t) = Qe^(-t/RC) with respect to time. In this case, R = 22 Ohms, C = F, and E(t) = 10 cos(31t) V.
First, we calculate the time constant T = RC: T = 22 F = 1/22 s. Then we substitute the given values into the equation q(t) = Qe^(-t/T) to get q(t) = 1e^(-t/(1/22)) C. To find the current, we differentiate q(t) with respect to time:
I = dQ/dt = -Q/T * e^(-t/T) = -(1/T) * e^(-t/T) = -(1/(1/22)) * e^(-t/(1/22)) = -22 * e^(-22t) A.