NEIEP Mechanics Practice Exam

How long will it take for a 5 microfarad capacitor to fully charge in a circuit with a resistance of 200K and a source voltage of 120 volts DC?

1. 2 seconds

2. 5 seconds

3. 10 seconds

4. 20 seconds

The correct answer is: 5 seconds

To determine how long it will take for a capacitor to fully charge in an RC circuit, we can use the time constant formula, which is given by the product of resistance (R) and capacitance (C). The time constant (τ) indicates how quickly the capacitor will charge to approximately 63.2% of the source voltage after one time constant and reaches near full charge (over 99%) after about five time constants. In this specific case, we have a capacitor of 5 microfarads (5 × 10^-6 F) and a resistor of 200,000 ohms (200K). First, we calculate the time constant (τ): \[ τ = R \times C = 200,000 \, \text{ohms} \times 5 \times 10^{-6} \, \text{farads} = 1 \, \text{second}. \] Next, to find the time it takes for the capacitor to charge close to its full capacity, we multiply the time constant by 5: \[ Total \, time \approx 5τ = 5 \times 1 \, \text{second} = 5 \, \text{