RC Circuit Question! Kinda Confused one Which Equation to Use.?

Question

Question: In a heart pacemaker, a pulse is delivered to the heart 81 times per minute. the capacistor that controls this pulsing rate discharges through a resistance of 1.8e6 ohms. one pulse is delivered every time the fully charged capacitor loses 63.2% of its original charge (CONFUSING!). what is the capacitance of the capacitor?

My Approach:
I went ahead and converted 81 pulses/minute to pulses/second (which is like 1.35 pulses/sec). I am having trouble plugging these numbers into an equation - q = q(initial)*e^(-t/RC). im not sure that's the equation to use. i would appreciate all the help i can get on this problem! even a fully solved problem would be cool.

Book Answer: 4.1e-7 F

Answer 1

The formula is
Q/Qi = exp[-t/RC] where exp is natural logarithm = 2.7…
[100-63.2]/100 = exp[(-60/81)/1.8x10^6xC]
0.368 = exp[-1] = exp[(-60/81)/1.8x10^6xC], this gives, [-1] = [(-60/81)/1.8x10^6xC]
and C = 4.1x10^(-7)

Answer 2

You need to figure the time constant first. Math rules for brackets still holds true.
The capacitor is discharged at the point where it has been charged to 63.2 % of the available energy provided to it. This is point is the most linear point on the rate of charge for a capacitor. It can be left to develop more of a charge, but the rate is no longer linear. For a good source of help, the timing techniques that Tektronix uses for their oscilloscopes might be a help to you. They use the capacitor-resistor technique in their 'scopes.This might help you to understand the concept. The discharge point, at 63.2% is a common trigger point for most circuits. You could change the discharge point if you wanted to to provide more energy to the device the pulse is going to.

Answer 3

Take your equation:
q = q(initial)*e^(-t/RC)

Calculate the period of pulses T0 = 60s/81 and rewrite the above written equation as

T0 / RC = -ln[ q(T0)/q(initial) ]

Solve this equation for C.


Now:

in time between the pulses T0 the charge of the capasitor
q(initial) loses 63.2% of its value, that is
q(T0) = q(initial) - 63.2% * q(initial) = 0.368 q(initial), or

q(T0)/q(initial) = 0.368.