91Ó°ÊÓ

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,

$\mathrm{Ï„}=RC$…â¶Ä¦â¶Ä¦â¶Ä¦â¶Ä¦â¶Ä¦.(1)

Where$\mathrm{Ï„}$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

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

And,

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

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

$$\begin{gathered} 0.833s=R×\left(2.50×{10}^{-8}F\right) \\ R=\frac{0.833s}{2.50×{10}^{-8}\mathrm{F}} \\ R=3.34×{10}^7\mathrm{Î\copyright }\left(\frac{1M\mathrm{Î\copyright }}{{10}^6\mathrm{Î\copyright }}\right) \\ R=33.4\mathrm{²ÑÎ\copyright } \\ \mathrm{Therefore},\mathrm{the}\mathrm{resistance}\mathrm{value}\mathrm{is}\mathrm{R}=33.4\mathrm{²ÑÎ\copyright }. \end{gathered}$$