Final answer:
The current i(t) in an RC circuit during the discharge of a capacitor is the derivative of the charge function, resulting in i(t) = -Q/τ * e-t/τ, where Q is the initial charge and tau is the time constant RC.
Step-by-step explanation:
The current i(t) flowing through the resistor R in an RC circuit when a capacitor is discharging can be determined using the voltage function v(t) = q0 * e-t/(RC). This equation shows that the voltage across the capacitor decreases exponentially with time. The current can be found by differentiating the charge on the capacitor with respect to time, since current (I) is the rate of change of charge (Q) over time (I = dQ/dt).
Given that the charge q(t) on the capacitor at any time t is Q * e-t/τ, where Q is the initial charge and τ (tau) is the time constant equal to RC, the time derivative of this function will give us the current i(t). Calculating this derivative yields i(t) = -Q/τ * e-t/τ. The negative sign indicates that the current is in the opposite direction during discharge compared to the charging process.