Elevator Mechanic Practice Exam

A capacitance of 5mf, a voltage of 120v, and a resistance of 200K ohm are present in a circuit. How long will it take to fully charge?

1. 10 to 15 time constants

2. 1 time constant

3. 5 time constants

4. 3 time constants

The correct answer is: 5 time constants

To determine how long it takes for a capacitor to fully charge in an RC (resistor-capacitor) circuit, we rely on the concept of time constants, denoted by the Greek letter tau (τ). The time constant is calculated as the product of resistance (R) in ohms and capacitance (C) in farads. In this case, the capacitance is 5 milliFarads (which is 5 x 10^-3 F) and the resistance is 200 K ohms (which is 200 x 10^3 ohms). The time constant τ can be calculated as follows: τ = R * C = (200 x 10^3 ohms) * (5 x 10^-3 F) = 1000 seconds. The voltage across the capacitor increases exponentially, approaching its maximum value with time. While it takes an infinite amount of time to reach full charge (100% of the applied voltage), practical applications often consider a capacitor to be effectively charged after a certain number of time constants. Conventionally, a capacitor is considered fully charged after 5 time constants, when it reaches about 99.3% of the maximum voltage. The correct choice of 5 time constants reflects this