30. Induction and Inductance

Consider the LR circuit shown below. Initially, both switches are open. Switch 1 is closed. a) What is the maximum current in the circuit after a long time? Then, S₁ is opened and S₂ is closed. b) What is the current in the circuit after 0.05s?

An LR circuit with L = 0.1 H and R = 10 Ω are connected to a battery with the circuit initially broken. When the circuit is closed, how much time passes until the current reaches half of its maximum value?

(II) It takes 2.85 ms for the current in an LR circuit to increase from zero to 0.75 its maximum value. Determine (a) the time constant of the circuit, (b) the resistance of the circuit if L = 31.0 mH.

(III) Two tightly wound solenoids have the same length and circular cross-sectional area. But solenoid 1 uses wire that is 1.5 times as thick as solenoid 2. (a) What is the ratio of their inductances? (b) What is the ratio of their inductive time constants? (Assume the only resistance in the circuits is that of the wire itself.)