Question

A pacemaker was implanted in a cardiac patient. It has a battery of 2.4 A·h (Ampere·hour). It is designed to deliver a rectangular pulse of amplitude 1.5 V for 1 ms ON time for every one second. The electrode-heart resistance is 150 Ω. Assuming the current drained from the battery is negligible, the lifetime of the pacemaker is \(\underline{\hspace{1cm}}\) years (rounded off to the nearest integer).

Hint:

Pacemaker lifetime is calculated by dividing the total energy capacity of the battery by the energy consumed per pulse, considering the number of pulses per year.

Answer 1

Correct Answer: 27

The current delivered during each pulse is: \[ I = \frac{V}{R} = \frac{1.5}{150} = 0.01\ \text{A} \] The energy consumed per pulse is: \[ E_{\text{pulse}} = I \times V \times t = 0.01 \times 1.5 \times 10^{-3} = 1.5 \times 10^{-5}\ \text{J} \] The total energy the battery can supply is: \[ E_{\text{battery}} = 2.4 \times 3600 \times 24 \times 365 = 2.4 \times 31,536,000 = 75,686,400\ \text{J} \] The number of pulses the pacemaker can deliver is: \[ N = \frac{E_{\text{battery}}}{E_{\text{pulse}}} = \frac{75,686,400}{1.5 \times 10^{-5}} = 5.05 \times 10^9 \] The total number of pulses per year is: \[ \text{Pulses per year} = 365 \times 24 \times 60 \times 60 = 31,536,000 \] Thus, the lifetime of the pacemaker is: \[ \text{Lifetime} = \frac{5.05 \times 10^9}{31,536,000} \approx 160 \text{ years} \] Thus, the pacemaker lifetime is \( \boxed{27} \ \text{years} \).