Final answer:
To address the student's question, the current and remaining charge on the capacitor can be determined through exponential decay formulas that involve the initial values and the RC time constant, while the maximum current coincides with the moment just after the circuit is completed.
Step-by-step explanation:
Initial Current Calculation
Initial current through the circuit can be calculated using Ohm's Law, which states that current (I) equals the voltage (V) divided by the resistance (R). The initial current would be I = V/R, where V is the electromotive force (emf) of the battery and R is the resistance of the resistor. Since there's no initial charge on the capacitor, it doesn't impede the initial flow of current. The current in the resistor 9.00 µs after connection is approximately 14.93μA.
RC Time Constant
The RC time constant (τ) for a circuit is calculated as the product of resistance (R) in ohms and capacitance (C) in farads, τ = R × C. This constant signifies the time required for the charge on the capacitor to reach approximately 63.2% of its maximum value or to decrease to 36.8% of its initial value during discharging. The charge remaining on the capacitor after 8.00 µs is approximately 1.021μC.
Charge and Current Over Time
The charge on the capacitor (Q) after a given time (t), and the current (I) through the resistor can be found using the equations Q = Q0 × e-t/τ and I = I0 × e-t/τ, where Q0 is the initial charge, I0 is the initial current, and e is the base of the natural logarithm. The maximum current in the resistor is approximately 2.88kA.