Question

What is the voltage across a capacitor in an RC circuit one millisecond after the switch is closed if the time constant of the circuit is 1 millisecond?

Option 1: 37 volts
Option 2: 47 volts
Option 3: 57 volts
Option 4: 67 volts

Answer 1

The voltage across a capacitor in an RC circuit one millisecond after the switch is closed can be calculated using the formula V = Vf(1 - e^(-t/RC)). In this case, with a time constant of 1 millisecond, the voltage will be approximately 0.632 or 63.2% of the final voltage.

Step-by-step explanation:

In an RC circuit, the voltage across a capacitor can be calculated using the formula V = Vf(1 - e-t/RC), where Vf is the final voltage, t is the time in seconds, R is the resistance, and C is the capacitance. The time constant, denoted by τ, is equal to RC.

In this case, the time constant is 1 millisecond or 0.001 seconds. After 1 millisecond, the voltage across the capacitor will be V = Vf(1 - e-0.001/0.001). Evaluating the equation gives us V = Vf(1 - e-1) ≈ Vf(1 - 0.368). So, the voltage across the capacitor one millisecond after the switch is closed will be approximately 0.632 or ≈ 63.2% of the final voltage.