Find the value of `t/tau` for which the current in an LR circuit builds up to (a) 90%, (b) 99% and ( c) 99.9% of the steady-state value.

Explanation

We know that , `i= i_0(1-e(-t//tau))`
`(a)=9)/(100)i_0=(1-e(-t//tau)`
`implies 0.9=1-e(-t//tau)`
` implies e(-t//tau)=0.1 `
taking in both sides
`In=e(-t//tau)`
`-(t/tau)=-2.3`
`implies (t/tau)=2.3`
`(b) (99)/(100) i_0=i_0(1-e^(-t//tau)`
`e(-t//tau)=0.01`