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

0.2854

Step-by-step 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`