How many time constants will elapse before the energy stored in the capacitor reaches half of its equilibrium value in a charging RC circuit ?

Explanation

`q = Q(1-e^-n)`
` 2q^2/2C = initial value `
` q^2/2C = final value`
` rArr 2q^2/2C = q^2/2C`
` rArr q^2 = q^2/2 rArr q= (sqrt (q^2/2))`
` rArr q/(sqrt 2) = q(1-e^-n)`
` rArr 1/sqrt 2 = 1-e^-n`
` rArr e^-n = 1 - (1/sqrt(2)) = ((sqrt(2))-1/sqrt(2))`
` rArr n= log ( sqrt(2) / ((sqrt 2)-1))` = 1.22 `