Question

A simple RC circuit with a voltage source and a switch is shown in Figure 25. In this circuit, the applied voltage is 100 VDC, the resistance is 100 kΩ, and the capacitance is 0.01 µF. Let's calculate the time constant for this circuit. Note that before we can substitute these values into our formula, we'll need to convert kilohms to ohms and microfarads to farads.

Option 1: 1 ms
Option 2: 10 ms
Option 3: 0.1 ms
Option 4: 100 ms

Answer 1

The time constant for the given RC circuit with a 100 kΩ resistor and a 0.01 µF capacitor is calculated by converting these values into standard units and using the formula T = RC, yielding a time constant of 1 ms.

Step-by-step explanation:

The time constant for an RC circuit is calculated using the formula T = RC, where R is the resistance in ohms, and C is the capacitance in farads. In the scenario provided, converting the given values from kilohms to ohms and microfarads to farads is required before substituting them into the formula. We thus have 100 kΩ as 100 × 103 ohms and 0.01 µF as 0.01 × 10-6 farads. Using these converted values, the time constant of the given RC circuit is calculated as:

T = (100 × 103 ohms) × (0.01 × 10-6 farads) = 1 millisecond (ms).

Therefore, the correct option for the time constant is 1 ms (Option 1).