A heart defibrillator being used on a patient has an RC time constant of 9.5 ms

Question

A heart defibrillator being used on a patient has an RC time constant of 9.5 ms due to the resistance of the patient's body and the capacitance of the defibrillator. Randomized Variables tau = 9.5 ms C = 7.5 mu F V = 14 k V If the defibrillator has an 75 mu F capacitance, what is the resistance of the path through the patient in k ohm? (You may neglect the capacitance of the patient's body and the resistance of the defibrillator.) If the initial voltage is 14 kV, how long does it take to decline to 6.00 x 10^2 V in ms? If the initial voltage is 14 kV, how long does it take to decline to 6.00 times 10^2 V in ms?

Explanation / Answer

here,

time constant , T = 0.0095 s

C = 7.5 uF

a)

let the resistance of the patient be R

R * C = T

R * 7.5 * 10^-6 = 0.0095

R = 1.27 kohm

b)

initial voltage , V0 = 14000 V

voltage at time t , V = 600 V

V = V0 * ( 1 - e^(-t/T))

600 = 14000 * ( 1- e^( - t/0.0095) )

t = 4.1 * 10^-4 s

t = 0.41 ms

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