A coil having an inductance `L` and a resistance `R` is connected to a battery of `emf epsilon`. Find the time elapsed before (a) the current reaches half its maximum value, (b) the power dissipated in heat reaches half its maximum value and (c) the magnetic field energy stored in the circuit reaches half its maximum value.

Options

A. `R/L ln [sqrt2/(sqrt-1)]`
B. `L/Rln [(sqrt2-1)/sqrt2]`
C. `L/R ln (sqrt2/(sqrt2-1))`
D. `R/L ln [(sqrt2-1)/sqrt2]`

Answer

C

Explanation

`1/2Li^2=1/2[1/2Li_0^2]`
`:. i=i_0/sqrt2=i_0(1-e^(-t//tau_L))`
`e^(t//tau_L)=1-1/sqrt2=(sqrt(2)-1)/(sqrt(2))`
`:. t/tau_L=ln (sqrt2/(sqrt2-1))`
`or t=tau_L ln (sqrt2/(sqrt2-1))`
`=L/R ln ((sqrt(2))/(sqrt(2)-1))`