23.10 RL Circuits

If you want a characteristic RL time constant of 1.00 s, and you have a $\text{500 }\Omega$ resistor, what value of self-inductance is needed?

A large superconducting magnet, used for magnetic resonance imaging, has a 50.0 H inductance. If you want current through it to be adjustable with a 1.00 s characteristic time constant, what is the minimum resistance of system?

Suppose you have a supply of inductors ranging from 1.00 nH to 10.0 H, and resistors ranging from $\text{0}.\text{100 }\Omega$ to $\text{1}.\text{00 M}\Omega$. What is the range of characteristic RL time constants you can produce by connecting a single resistor to a single inductor?

What percentage of the final current $I_{\text{0}}$ flows through an inductor $L$ in series with a resistor $R$, three time constants after the circuit is completed?

(a) Use the exact exponential treatment to find how much time is required to bring the current through an 80.0 mH inductor in series with a $\text{15}.\text{0 }\Omega$ resistor to 99.0% of its final value, starting from zero. (b) Compare your answer to the approximate treatment using integral numbers of $\tau$. (c) Discuss how significant the difference is.