High School

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Which of the following statements accurately describes the charging of a capacitor in a circuit after five time constants (five milliseconds in this example)?

A. The capacitor is fully charged to 100 percent of its full voltage, and the voltage across the resistor is 0 VDC.

B. The capacitor is fully charged to 99.3 percent of its full voltage, and the voltage across the resistor is 0.7 VDC.

C. The capacitor is partially charged, and the voltage across the resistor remains at its initial value.

D. The capacitor is fully charged to 100 percent of its full voltage, and the voltage across the resistor is 0.7 VDC.

Answer :

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.

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.

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Rewritten by : Barada