Final answer:
The characteristic time τ of a solenoid is the ratio of its inductance L to resistance R. This concept is crucial for understanding the current change in an RL circuit, with the expression given by τ = L/R.
Step-by-step explanation:
The characteristic time τ of a solenoid is defined as the ratio of the inductance L to the resistance R. It represents the time constant for an RL circuit and is crucial for predicting how quickly the current will change within the circuit. To calculate this time constant, one should know both the inductance L, which is influenced by the physical properties of the solenoid, and the resistance R in the circuit. The expression for the characteristic time τ is:
τ = L/R.
For example, if a solenoid has an inductance of 7.50 mH (millihenries) and is placed in series with a 3.00 Ω (ohm) resistor, the characteristic time τ would be calculated as follows:
τ = 7.50 mH / 3.00 Ω = 2.50 ms (milliseconds).
This value represents how long it will take for the current to change significantly within the circuit.