In a series LR circuit connected to a DC source of EMF E at time t = 0, what fraction of the maximum steady-state current (I₀ = E/R) is established after a time interval equal to one inductive time constant (τ = L/R)?

Answer and explanation

Correct answer: C. Approximately 63.2% (1 - 1/e)

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  1. Step 1: The growth of current in a series LR circuit is governed by the differential equation yielding: , where is the inductive time constant.
  2. Step 2: At time , the ratio .
  3. Step 3: Substitute into the current expression:
  4. Step 4: Since , .
  5. Step 5: Thus, or .
Answer
Approximately 63.2% (1 - 1/e)
Why not the others: 'Approximately 36.8% (1/e)' is the fraction of current remaining during decay (), or the uncompleted portion of growth; 'Approximately 50.0%' represents the half-life (); '100.0%' is only achieved asymptotically as .

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