Question

A defibrillator delivers a jolt of electrical energy to restart a heart that is either stopped or undergoing ventricular defibrillation -- a rapid irregular beating. This energy is supplied by a charged capacitor. Consider a 299 μF capacitor charged to 2750 V in a defibrillator.


A 5000 V power supply is used to charge the capacitor through a 36.7 kΩ resistor. If the capacitor is initially uncharged, how much time does it take to charge the capacitor to 2750 V?

Answer 1

T = R C = 36.7 * 10³ * 299 * 10^-6 = 10.97 s

V = V₀ * (1 - e^-t/T)

2750 = 5000 (1 - e^-t/10.97)

(1 - e^-t/10.97) = 2750 / 5000

1 - (2750 / 5000) = e^-t/10.97

-t/10.97 = ln (0.45)

t = 8.75 s