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# Time Constant 2

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#### herbymcduff

##### New Member
It doesn't matter what circuit, a RC, or a 555 astable, I just want to know how the .693 in the time constant formula came from. :roll:

Dear herbymcduff,
It is not necessary to post every new reply of yours as a new topic. This forum has a facility to append your questions/anserwer within the same topic using the Big Blue/Orange colored button with "Post Reply" caption on it. Please use this facility next time you post the reply related to same topic and do not create a new topic as a reply to other post. Hope you got my point. :wink:

The charging equation of capacitor is given by:
q = qf{1 - e-t/RC}

Here,
q=charge at given instant in capacitor
qf=final charge in capacitor
t=time
R=resistor
C=cap. value

Now the half-life (qf/2) of the circuit is calculated as
qf/2 = qf{1 - e-t/RC}
1/2 = 1 - e-t/RC
0.5 - 1 = - e-t/RC
-0.5 = - e-t/RC
0.5 = e-t/RC
ln(0.5)=ln(e-t/RC)
ln(0.5)=-t/RC
t=-ln(0.5)RC
t=0.693RC

Hope now your point is clear.

thanks

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