NEIEP Mechanics Practice Exam

What is the time constant for a circuit with 150KOhms and a 2 microfarad capacitor?

1. 0.1 seconds

2. 0.3 seconds

3. 0.5 seconds

4. 1.0 seconds

The correct answer is: 0.3 seconds

The time constant of an RC (resistor-capacitor) circuit is determined using the formula: \[ \tau = R \times C \] where \( \tau \) (tau) is the time constant in seconds, \( R \) is the resistance in ohms, and \( C \) is the capacitance in farads. In this case, the resistance is 150,000 ohms (150KΩ) and the capacitance is 2 microfarads (2μF), which needs to be converted to farads. This can be done using the conversion factor where 1 microfarad equals \(10^{-6}\) farads: \[ C = 2 \, \text{μF} = 2 \times 10^{-6} \, \text{F} \] Now substituting the values into the time constant formula: \[ \tau = 150,000 \, \Omega \times 2 \times 10^{-6} \, \text{F} \] Calculating this gives: \[ \tau = 150,000 \times 2 \times 10^{-6} = 0.3 \, \text{