Question

Which of the following statements regarding the time constant of a circuit is correct?

Option 1: One millisecond after the switch is closed, the capacitor has charged to 37 percent of the supply voltage.
Option 2: One millisecond after the switch is closed, the capacitor has charged to 100 percent of the supply voltage.
Option 3: After one time constant, the capacitor reaches its full charge, which is 100 percent of the supply voltage.
Option 4: After five time constants, the capacitor reaches its full charge, which is 100 percent of the supply voltage.

Answer 1

Option 1: One millisecond after the switch is closed, the capacitor has charged to 37 percent of the supply voltage.

Step-by-step explanation:

The correct statement regarding the time constant of a circuit is Option 1: One millisecond after the switch is closed, the capacitor has charged to 37 percent of the supply voltage.

The time constant of an RC circuit is the time it takes for the voltage across the capacitor to reach approximately 63.2% of its final voltage. This can be calculated using the formula:

Time constant (T) = R x C

For the given circuit, after one time constant, the capacitor will reach approximately 37% of the supply voltage, not the full charge as mentioned in Option 3 and Option 4, which are incorrect.