After two time constants, to what percentage of the starting voltage is a capacitor in an RC circuit discharged?

After two time constants, to what percentage of the starting voltage is a capacitor in an RC circuit discharged?

• A. 63.2%
• B. 86.5%
• C. 13.5%
• D. 30%

Answer: (C)

In an RC (resistor-capacitor) circuit, the discharge of a capacitor follows an exponential decay pattern described by the time constant, which is the product of the resistance (R) and capacitance (C) values in the circuit. The time constant is the time it takes for the capacitor to discharge approximately 63.2% of its initial charge. After one time constant, the voltage across the capacitor is about 36.8% of the initial voltage. After a second time constant (which totals two time constants), the discharge reaches approximately 86.5% of the initial voltage. This means that only about 13.5% of the initial voltage remains across the capacitor. The correct answer illustrates that after two time constants in a discharging RC circuit, the capacitor's voltage is reduced to 13.5% of its starting voltage, showcasing the expected exponential behavior as the capacitor discharges. This percentage accurately reflects the time constant's influence on the discharge rate within the given timeframe.

In an RC (resistor-capacitor) circuit, the discharge of a capacitor follows an exponential decay pattern described by the time constant, which is the product of the resistance (R) and capacitance (C) values in the circuit. The time constant is the time it takes for the capacitor to discharge approximately 63.2% of its initial charge.

After one time constant, the voltage across the capacitor is about 36.8% of the initial voltage. After a second time constant (which totals two time constants), the discharge reaches approximately 86.5% of the initial voltage. This means that only about 13.5% of the initial voltage remains across the capacitor.

The correct answer illustrates that after two time constants in a discharging RC circuit, the capacitor's voltage is reduced to 13.5% of its starting voltage, showcasing the expected exponential behavior as the capacitor discharges. This percentage accurately reflects the time constant's influence on the discharge rate within the given timeframe.