A heart pacemaker fires 72 times a minute, each time a 25.0-nF capacitor is charged (by a battery in series with a resistor) to 0.632 of its full voltage. What is the value of the resistance?

A capacitor is an electrical energy storage device that operates in an electric field. It's a two-terminal passive electrical component. Capacitance is the term used to describe the effect of a capacitor.

A heart pacemaker fires 72 times a minute, each time a 25.0 nF capacitor is charged (by a battery in series with a resistor) to 0.632 of its full voltage.

The time constant for the RC circuit is given as,

$\tau =RC$……………….(1)

Where$\tau$is the time constant, is the resistance of the circuit, and is the capacitance of the circuit.

Given that the pacemaker in your heart beats 72 times per minute,

As a result, the pacemaker's time constant is calculated as

$$\begin{gathered} \tau =\frac{1min}{72}\times \frac{60\mathrm{s}}{1\min } \\ =0.833s \end{gathered}$$

And,

$C=25.0nf\left(\frac{{10}^{-9}\mathrm{F}}{1\mathrm{nF}}\right)=2.50\times \times {10}^{-8}\mathrm{F}$

Substitute the given values in the expression (1), and we get,

$$\begin{gathered} 0.833s=R\times \left(2.50\times {10}^{-8}F\right) \\ R=\frac{0.833s}{2.50\times {10}^{-8}\mathrm{F}} \\ R=3.34\times {10}^7\Omega \left(\frac{1M\Omega }{{10}^6\Omega }\right) \\ R=33.4\mathrm{M\Omega } \\ \mathrm{Therefore},\mathrm{the}\mathrm{resistance}\mathrm{value}\mathrm{is}\mathrm{R}=33.4\mathrm{M\Omega }. \end{gathered}$$