How many seconds will it take for a capacitor in an RC circuit to completely charge if the circuit has a time constant of 0.05 seconds?

In an RC circuit, the charging of a capacitor is characterized by the time constant, which is the product of the resistance (R) and the capacitance (C) in the circuit. The time constant indicates how quickly the capacitor charges to approximately 63.2% of its maximum voltage after one time constant has elapsed.

However, to consider how long it takes for the capacitor to reach its maximum charge, we often refer to the concept of 'complete' charging, which technically never occurs mathematically, as a capacitor asymptotically approaches the supply voltage but never quite reaches it. Practically, though, we can consider it effectively charged after about four to five time constants.

Given a time constant of 0.05 seconds, after one time constant, the capacitor will reach about 63.2% of the maximum charge. After two time constants (0.10 seconds), it will reach about 86.5%, and after three time constants (0.15 seconds), it will be at about 95%, and close to 99% after four time constants (0.20 seconds).

By the time we reach approximately 0.25 seconds (which corresponds to five time constants), the capacitor is considered to be completely