Chapter 18, Problem 37P

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

Chapter
Section

### College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
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 Î”V is 775â€‰V , Supplied voltage Îµ is 1250â€‰V , and Time elapsed t is 1.50â€‰s , The capacitance of given Capacitor CÂ  is 8.00â€‰ÂµF and the time constant Ï„ is 1.55â€‰s .

Explanation:

Formula to calculate time constant Ï„ is,

While charging, the voltage across capacitor is given by

Î”V(t)=Îµ(1âˆ’e(âˆ’tÏ„))

On rearranging

Ï„=âˆ’tlnâ€‰(1âˆ’Î”V(t)Îµ)

• Î”V(t) is the voltage across the capacitor,
• t is the elapsed time since the removal of the supply voltage,
• Ï„ is the time constant,
• Îµ is the supplied voltage,

Substitute 775â€‰V for Î”V(t) , 1250â€‰V for Îµ , and 1

(b)

To determine
The voltage across the capacitor after 5.00ms

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