Final answer:
The time constant of the RL circuit with a 0.5H inductor and a 10,000Ω resistor is calculated using the formula τ = L/R, resulting in a time constant of 50 microseconds.
Step-by-step explanation:
The time constant of an RL circuit is given by the formula τ = L/R, where τ (tau) represents the time constant, L is the inductance of the inductor, and R is the resistance of the resistor. In the given problem, a 0.5H inductor is connected to a 10,000Ω resistor. To calculate the time constant of the circuit, you divide the inductance by the resistance.
Using the formula, we have:
τ = L/R = 0.5H / 10,000Ω
τ = 0.00005 seconds or 50 microseconds
Therefore, the time constant of the circuit is 50 microseconds.