t1/2 means that the voltage (or charge) of the system will increase to half more

Question

t1/2 means that the voltage (or charge) of the system will increase to half more of what is left in a time equal to t1/2 seconds. Therefore if a system is already at half charge (t1/2 seconds after starting) then after t1/2 more seconds the system will be charged to 50% plus half of 50%. That is 25% more, or 75% of the entire charge.Let's say that four t1/2's have gone by. That means that the charge (or voltage) is at (50% + 1/2*50% + 1/2*1/2*50% + 1/2*1/2*1/2*50%) = 93.75% of maximum charge. Yikes! Now look in your manual for a more simple mathematical derivation of this concept. 9. Given t1/2 to be 0.0124 seconds, how long should it take to reach 93.75% of maximum charge? time =

Explanation / Answer

The system takes 0.0124 s to reach 50% of maximum charge.

To reach 75% it takes 0.0124 s more.

93.75 = 50*(1+0.5+0.52 + 0.53)

as there are 4 terms in the sum and each term takes 0.0124 s

so total time taken is 0.0124*4=0.0496 s

or in general, this is the sum of geometric progression. Whose sum goes as Sn = a(1+rn)/(1-r) here a is 50

and r is 0.5.

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