Final answer:
The initial current i0 through a resistor immediately after closing a switch in a circuit can be determined by Ohm's law and assuming an uncharged capacitor, the current is calculated as Q/C divided by R. The current goes to zero when the capacitor is fully charged. Opening the switch results in the capacitor discharging through the resistor, influenced by the RC time constant.
Step-by-step explanation:
Initial current through a resistor when a switch is closed in a circuit can be determined using Ohm's law and the characteristics of the capacitor in the circuit. Right after the switch is closed, if we assume the capacitor is initially uncharged, the current i0 would effectively be the voltage across the resistor divided by the resistance, as per Ohm's law. This assumes that at t=0, the capacitor has no voltage across it and therefore does not affect the initial current. The formula for the initial current i0 would be i0 = Q/C divided by R, where Q is the initial charge (which is 0 for an uncharged capacitor), R is the resistance, and C is the capacitance.
When the capacitor is fully charged, the current through the resistor is zero since the capacitor acts like an open circuit, blocking DC current flow.
Opening the switch after the capacitor has been charged will cause the capacitor to discharge through the resistor, following an exponential decay pattern determined by the RC time constant.
The RC time constant is defined as the product of the resistance (R) and the capacitance (C). It represents the time required for the voltage across the capacitor to reach approximately 63% of its final value, or conversely, to decay to 37% of its initial value when discharging.