The choice of the fraction Delta V(t)/Delta V(0) is arbitrary. We could choose i

Question

The choice of the fraction Delta V(t)/Delta V(0) is arbitrary. We could choose it to be 1/2 and usually do when dealing with radioactive decay. If we make this choice then the time for the voltage to fall to half of its initial value is called the half-life (and is written t_1/2). There is a relation between half-life and time constant that can be shown using Delta V(t)/Delta V(0) = e^-t/tau. If t = t_1/2 then Delta V(t_1/2)/Delta V(0) = 1/2. Now use Delta V(t)/Delta V(0) = e^-t/tau to show that t_1/2 = tau ln2.

Explanation / Answer

V(t)/V(0)=e-t/tow

at t=t1/2 above value equals to 1/2

e-t/tow =1/2

ln2=t/tow

t=ln2*tow

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