Question

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?

Answer 1

Answer:

0.2854

Explanation:

The Energy stored in coil is given by

U=$\frac{1}{2}$L$I^{2}$

U=0.565Uo

$(\frac{1}{2} )L(i^{2} )=(0.565)(\frac{1}{2} )L(io^{2} )$

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

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

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

$e^{-2t/T}=0.565$

Apply log: both sides we get

$\frac{-2t}{T}=-0.5709$

$\frac{t}{T}=0.2854$