PHYSICS HIGH SCHOOL

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 0.565 its steady-state value?

Answers

Answer 1

Answer:

Answer:

0.2854

Explanation:

The Energy stored in coil is given by

U= $(1)/(2)$ L $I^(2)$

U=0.565Uo

$((1)/(2) )L(i^(2) )=(0.565)((1)/(2) )L(io^(2) )$

$(i^(2) )=(0.565)(io^(2) )$

$(ioe^(-t/T) )^(2)=(0.565) (io)^(2)$

$(io)^(2)e^(-2t/T)=(0.565)(io)^(2)$

$e^(-2t/T)=0.565$

Apply log: both sides we get

$(-2t)/(T)=-0.5709$

$(t)/(T)=0.2854$

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