An inductor carrying steady current I₀ is disconnected from its battery and discharges through resistance R. Find the time for its magnetic energy to become one-fourth of the initial value.
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Question

An inductor carrying steady current I₀ is disconnected from its battery and discharges through resistance R. Find the time for its magnetic energy to become one-fourth of the initial value.

G1 Physics · Accepted Answer

I=I₀e^(−Rt/L), so U/U₀=e^(−2Rt/L). Setting this to 1/4 gives t=(L/R)ln2.