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

`2* 10^(-3)\ C`

6000

1.2 J

`3.33* 10^(-6)\ F`

Step-by-step explanation:

I = Current = 1 A

t = Time = 2 ms

n = Number of electrocyte

V = Voltage = 100 mV

Charge is given by

`Q=It\\\Rightarrow Q=1* 2* 10^(-3)\\\Rightarrow Q=2* 10^(-3)\ C`

The charge flowing through the electrocytes in that amount of time is
`2* 10^(-3)\ C`

The maximum potential is given by

`V_m=nV\\\Rightarrow n=(V_m)/(V)\\\Rightarrow n=(600)/(100* 10^(-3))\\\Rightarrow n=6000`

The number of electrolytes is 6000

Energy is given by

`E=Pt\\\Rightarrow E=V_mIt\\\Rightarrow E=600* 1* 2* 10^(-3)\\\Rightarrow E=1.2\ J`

The energy released when the electric eel delivers a shock is 1.2 J

Equivalent capacitance is given by

`C_e=(Q)/(V_m)\\\Rightarrow C_e=(2* 10^(-3))/(600)\\\Rightarrow C_e=3.33* 10^(-6)\ F`

The equivalent capacitance of all the electrocyte cells in the electric eel is
`3.33* 10^(-6)\ F`