Final answer:
The initial value of current in an RC circuit is inversely proportional to the resistance, with a lower resistance resulting in a higher initial current and a quicker charge time for the capacitor. The time to reach steady state is determined by the RC time constant (T = RC), which increases with higher resistance.
Step-by-step explanation:
The initial value of the current in an RC circuit can be formulated by Ohm's law, which states that current (I) is the voltage (V) divided by resistance (R), so Io = V/R. Considering this, the smaller the resistance, the larger the initial current when the switch is closed in a circuit with an initially uncharged capacitor. Over time, as the capacitor charges, the current gradually decreases until it reaches zero, at which point the circuit is said to have reached its steady state. The internal resistance of the battery, as well as the resistances of the capacitor and the connecting wires, are all included in R.
The RC time constant is symbolic of the time it takes for the current to decrease to 1/e of its initial value, with T = RC. If resistance is increased, the RC time constant increases and thus the time to reach steady state also increases, meaning the circuit reaches a steady state more slowly. Conversely, a lower resistance implies a faster charge time for a given capacitor and a quicker approach to steady state. The internal resistance of the battery affects the total resistance and can significantly alter current values and charge times as it changes.