Please help with this capacitance problem You\'re designing an external defibril

Question

Please help with this capacitance problem

You're designing an external defibrillator that discharges a capacitor through the patient's body, providing a pulse that stops ventricular fibrillation. Specifications call for a capacitor storing 250 J of energy; when discharged through a body with R = 40 ohm transthoracic resistance, the capacitor voltage is to drop to half its initial value in 10 ms. Determine the capacitance (to the nearest ) 10 muF). Express your answer to two significant figures and include the appropriate units. Determine initial capacitor voltage (to the nearest 100 V) that meet these specs. Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

A) Let T is the time constant.

while discharging voltage across capacitor, at time t

V = Vmax*e^(-t/T)

Vmax/2 = Vmax*e^(-t/T)

0.5 = e^(-t/T)

ln(0.5) = -t/T

T = -t/ln(0.5)

= -10*10^-3/ln(0.5)

= 14.4*10^-3 s

now Apply, T = R*C

==> C = T/R

= 14.4*10^-3/40

= 3.6*10^-4 F or 360 micro F

B) Umax = 0.5*C*Vmax^2

==> Vmax = sqrt(2*Umax/C)

= sqrt(2*250/(3.6*10^-4))

= 1179 volts

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