Question

An electric eel (Electrophorus electricus) can produce a shock of up to 600 V and a current of 1 A for a duration of 2 ms, which is used for hunting and self-defense. To perform this feat, approximately 80% of its body is filled with organs made up by electrocytes. These electrocytes act as self-charging capacitors and are lined up so that a current of ions can easily flow through them.

a) How much charge flows through the electrocytes in that amount of time?
b) If each electrocyte can maintain a potential of 100 mV, how many electrocytes must be in series to produce the maximum shock?
c) How much energy is released when the electric eel delivers a shock?
d) With the given information, estimate the equivalent capacitance of all the electrocyte cells in the electric eel.

Answer 1

(a) The charge flows through the electrocytes is,

$$ \begin{aligned} q &=i t \\ &=(1)\left(2 \times 10^{-3}\right) \\ &=2 \times 10^{-3} \mathrm{C} \end{aligned} $$

(b) The maximum potential is,

$$ \begin{aligned} V_{\max } &=n V \\ n &=\frac{V_{\max }}{V} \\ &=\frac{600}{100 \times 10^{-3}} \\ &=6000 \end{aligned} $$

(c) The energy released when the electric eel delivers a shock is,

$$ \begin{aligned} E &=P t \\ &=\left(V_{\max } I\right) t \\ &=(600)(1)\left(2 \times 10^{-3}\right) \\ &=1.2 \mathrm{~J} \end{aligned} $$

(d) The equivalent capacitance of the electrocyte cells is,

$$ \begin{aligned} C_{\text {equ }} &=\frac{q}{V_{\max }} \\ &=\frac{2 \times 10^{-3}}{600} \\ &=3.33 \times 10^{-6} \mathrm{~F} \end{aligned} $$