Final answer:
The question involves an RC circuit to determine the resistance value in a heart pacemaker. By knowing the pacemaker fires 72 times a minute and the capacitor charges to 0.632 of full voltage, we can deduce one time constant is involved. Calculating using the time constant formula and given capacitance, the resistance can be determined.
Step-by-step explanation:
The question pertains to the functioning of a heart pacemaker, which involves a basic understanding of RC circuits in physics. An RC circuit consists of a resistor (R) and a capacitor (C) connected to a power supply. In the context of the pacemaker, the capacitor is charged to a certain fraction of its full voltage and then discharges to provide an electrical stimulus to the heart. The amount of time it takes for the capacitor to charge up to a certain percentage of its maximum voltage is known as the RC time constant (τ = RC).
To find the value of the resistance for the pacemaker firing 72 times a minute and the capacitor charging to 0.632 of its full voltage, we first note that 0.632 is approximately equal to 1 - (1/e), where e is the base of the natural logarithm. This corresponds to one time constant. Since the pacemaker fires 72 times per minute, there is approximately 1/72 minutes, or 5/3 seconds, per cycle. The time constant τ is therefore 5/3 seconds. Given that the capacitance (C) is 25.0 nF, we can use the relationship τ = RC to find the resistance (R): τ = RC → R = τ / C = (5/3) / (25.0 × 10^-9 F), which will yield the resistance value in ohms (Ω).