Show that the time for the voltage in the RC circuit to rise to (Vo/2) "half-max" is t1/2 = T ln 2

Answer 1

Time constant T=RC

U =U₀exp(-t/RC)
U/U₀ =exp(-t/RC)
U₀/2U₀ =1/2 = exp(-t/RC)
ln(1/2) = -t/RC)
ln(1/2) =- ln2
ln2 = t/RC
t=RC•ln2=T•ln2