At t = 0, a battery is connected to a series arrangement of a resistor and an inductor. At what multiple of the inductive time constant will the energy stored in the inductor's magnetic field be 0.500 of its steady-state value?

Explanation

To solve the problem, we need to find the time at which the energy stored in the inductor's magnetic field is 0.5 times its steady-state value. Here’s the step-by-step solution:

### Step 1: Understand the steady-state energy in the inductor
The energy stored in an inductor is given by the formula:
\[ U = \frac{1}{2} L I^2 \]
where \( U \) is the energy, \( L \) is the inductance, and \( I \) is the current through the inductor.
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