(-) WebAssign-PHY 213 SP2018. × y Homework #5 r chegg Study | Guided Solutio G h

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(-) WebAssign-PHY 213 SP2018. × y Homework #5 r chegg Study | Guided Solutio G how to zoom in on mac-Goo × × csecure l https://www.webassign.net/web/Student/Assignment-Responses/last?dep-18310153 The figure below shows a simplified model of a cardiac defibrillator, a device used to resuscitate patients in ventricular fibrillation. torso When the switch S is toggled to the left, the capacitor C charges through the resistor R. When the switch is toggled to the right, the capacitor discharges current through the patient's torso, modeled as the resistor Rtorso, allowing the heart's normal rhythm to be reestablished HINT The voltage across a charging capacitor is V-E(1-e-t/(RQ) and the voltage across a discharging capacitor is v-avra,e-t/(RC) Click the hint button again to remove this hint. (a) If the capacitor is initially uncharged with C = 7.75 F and 8-1230 V, find the value of R (in ohms) required to charge the capacitor to a voltage of 765 V in 1.30 s. (b) If the capacitor is then discharged across the patient's torso with Rtoro-1260 , calculate the voltage (in V) across the capacitor after 4.00 ms. Need Help? Read itWatch t Watch It

Explanation / Answer

a) Let T is the time constant of te circuit,

while charging a capacitor the volathe across the capacitor at time t,

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

765 = 1230*(1 - e^(1.3/T))

765/1230 = 1 - e^(-1.3/T)

e^(-1.3/T) = 1 - 765/1230

e^(-1.3/T) = 0.378

-1.3/T = ln(0.378)

T = -1.3/ln(0.378)

R*C = 1.336

R = 1.336/C

= 1.336/(7.75*10^-6)

= 1.72*10^5 ohms

b) Time constant whole disharging, T = R_torso*C

= 1260*7.75*10^-6

= 9.77 ms

Voltage across the capacitor,

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

= 1230*e^(-4/9.77)

= 817 V

if capacitor discharges from 765 V,

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

= 765*e^(-4/9.77)

= 508 V

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