   Chapter 18, Problem 37P

Chapter
Section
Textbook Problem

Figure P18.37 shows a simplified model of a cardiac defibrillator, a device used to patients in ventricular fibrillation. 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. (a) If the capacitor is initially uncharged with C = 8.00 µF and ε = 1250 V, find the value of R required to charge the capacitor to a voltage of 775 V in 1.50 s. (b) If the capacitor is then discharged across the patient’s torso with, Rtorso = 1250 Ω, calculate the voltage across the capacitor after 5.00 ms. Figure P18.37

(a)

To determine
The value of resistor R to charge the capacitor.

Explanation

Given Info: Voltage to charge the capacitor ΔV is 775V , Supplied voltage ε is 1250V , and Time elapsed t is 1.50s , The capacitance of given Capacitor C  is 8.00µF and the time constant τ is 1.55s .

Explanation:

Formula to calculate time constant τ is,

While charging, the voltage across capacitor is given by

ΔV(t)=ε(1e(tτ))

On rearranging

τ=tln(1ΔV(t)ε)

• ΔV(t) is the voltage across the capacitor,
• t is the elapsed time since the removal of the supply voltage,
• τ is the time constant,
• ε is the supplied voltage,

Substitute 775V for ΔV(t) , 1250V for ε , and 1

(b)

To determine
The voltage across the capacitor after 5.00ms

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