a heart pacemaker (a series RC circuit with a batter) needs to beat 400 times pe

Question

a heart pacemaker (a series RC circuit with a batter) needs to beat 400 times per minute (this one is from imaginary creature, not humans). it sends a pulse to the heart every time the voltage across a capacitor reaches 3.0 volts, at which moment the capacitor instantly and fully discharges, and the process repeats. the battery voltage is 20 volts, and the resistor in the series RC circuit has a value of 2000 ohms. find the value of the capacitance needed.

Explanation / Answer

C*dv/dt + V/R=0 =>C*dv/v=-dt/R Integrating both sides we get C*ln(v(t)/v(0)) =-t/R [v(0)=20] C*ln3/20=-1/2000 =>C=2.6*10^-4 F

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