Final answer:
The time required for the current in an inductor to reach its full Ohm's law value is called the inductive time constant, which depends on the inductance and resistance in the circuit. Option A is correct.
Step-by-step explanation:
The time required for current in an inductor to reach its full Ohm's law value is called the inductive time constant. The inductive time constant (τ, the Greek letter tau) is determined by the inductance (L) and the resistance (R) in the circuit.
According to Ohm's law for an inductor, the greater the inductance (L), the larger the time constant τ is because a large inductance effectively opposes changes in current. Conversely, the smaller the resistance (R), the larger τ is, as a smaller resistance leads to a larger final current, necessitating a more substantial change to reach equilibrium.
Hence, both a large inductance and a small resistance lead to a more considerable amount of energy being stored in the inductor and consequently requiring more time for the current to reach 90% of its final value.
By using the provided expressions, for a circuit where it takes 5.0 seconds for the current to increase to 90% of its final value, you can calculate the inductive time constant. Specifically, if R is given as 20 Ω (ohms) and L needs to be found, you would use these values in conjunction with the established formulas to determine L. It's also possible to assess how the replacement of a 20-Ω resistor with a 100-Ω resistor influences the time taken for current to reach 90% of its final value.