Final answer:
The maximum current in the RL circuit is 40.9 mA. The time constant is 0.386 s. The equations that relate the current to time and how to calculate the time at specific current levels are provided.
Step-by-step explanation:
To calculate the maximum current imax in an RL circuit, we can use the equation imax = ε/R, where ε is the voltage of the battery and R is the resistance. In this case, ε = 9.0 V and R = 220 Ω. Substituting these values into the equation, we get imax = 9.0 V / 220 Ω = 0.0409 A. To convert this to milliamps, we multiply by 1000, giving us a maximum current of 40.9 mA.
The time constant (t) of an RL circuit is given by the equation t = L/R, where L is the inductance and R is the resistance. In this case, L = 85 mH and R = 220 Ω. Substituting these values, we get t = (85 mH)/(220 Ω) = 0.386 s.
The equation that relates the current as a function of time i(t) to the maximum current imax can be written as i(t) = imax(1 - e^(-t/t)), where t is the time in seconds. This equation shows how the current in the circuit changes over time.
To calculate the time at which the current has a value of 50% of imax, we substitute this value into the equation i(t) = imax(1 - e^(-t/t)) and solve for t. Similarly, to calculate the time at which the current has a value of 99% of imax, we substitute this value into the equation and solve for t. These values will give us the times in seconds when the current reaches the specified percentages of imax.