Final answer:
The initial current through a circuit right after the switch is closed is determined by Ohm's Law and equals the battery voltage divided by the resistance. As the capacitor charges, this current decreases to zero, and the voltage across the capacitor equals the battery voltage at a steady state.
Step-by-step explanation:
The initial current immediately after the switch is closed in a circuit consisting of a battery, resistor, and an uncharged capacitor is driven by the full voltage of the battery. At time t=0 s, the capacitor behaves like a short circuit, meaning the initial current (I) is given by Ohm's Law, I=V/R, where V is the battery voltage and R is the resistance in the circuit. However, as the capacitor begins to charge, the current will decrease until it eventually reaches zero in the steady state when the capacitor is fully charged, and no current flows through it. The voltage across the capacitor in this steady state will be equal to the battery voltage, as no current means there is no voltage drop across the resistor.