Final answer:
After five time constants, the capacitor is not fully charged but very close to it, at 99.3% of the maximum voltage, with the voltage across the resistor being practically 0 VDC, making Option 2 the accurate statement.
The correct option is Option 2: The capacitor is fully charged to 99.3 percent of its full voltage, and the voltage across the resistor is 0.7 VDC.
Step-by-step explanation:
To accurately describe the charging of a capacitor in a circuit after five time constants, we should consider the exponential nature of the charge and discharge process.
Looking at the options provided, we can use the equation Vc = V(1 - e^{-t/RC}) to determine the capacitor's voltage after a given number of time constants, where V is the final voltage, t is the time, and RC is the time constant.
After five time constants (5RC), the voltage across the capacitor (Vc) is very close to the maximum voltage (V), approximately 99.3% of full charge.
Therefore, the correct statement is Option 2: The capacitor is fully charged to 99.3 percent of its full voltage, and the voltage across the resistor is essentially 0 VDC because voltage across the resistor equals total voltage minus capacitor's voltage, which is negligible.
It's important to note that we mention the voltage across the resistor being essentially 0 VDC in a practical sense, although theoretically, it could be a very small value, the difference between the supply voltage and the capacitor's voltage.
The correct option is Option 2: The capacitor is fully charged to 99.3 percent of its full voltage, and the voltage across the resistor is 0.7 VDC.