In a heart pacemaker, a capacitor of 3.43x10^-7 F discharges through a 1.80x10^6

Question

In a heart pacemaker, a capacitor of 3.43x10^-7 F discharges through a 1.80x10^6 ohm resistor. One pulse is delivered to the heart each time the charge on the capacitor is 1/4 of its initial value a) What is the time constant for this circuit? b) What fraction of its initial energy is stored in the discharging capacitor at the instant the charge on the capacitor is 1/4 of its value? c) How many pulses does the pacemaker deliver to the heart each minute? (Assume that after a pulse is delivered to the heart, the time needed to recharge the capacitor is negligible compared with the discharge time, that is, assume that the capacitor is instantly recharged after delivering a pulse.) 1.80 x 1 06 3.43 x 107 F

Explanation / Answer

a)

Time constant = T = RC = 3.43 x 10-7 x 1.80 x 106 = 0.62 sec

b)

Qi = Q = initial charge

Qf = Q/4 = final charge

ratio of energy stored is given as

Ei/Ef = Qi2/Qf2

Ei/Ef = 16

Ef = 0.0625 Ei

c)

Q = Qo e-t/T

given , Q = Qo/4

Qo/4 = Qo e-t/T

0.25 = e-t/0.62

t = 0.86 = time for one pulse

number of pulse = Total time / t = 60 /0.86 = 69 pulse

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.