How an Electric Eel Stuns its Prey

Electricity and Magnetism Level 2

Inside the electric eel there is a special organ that contains many EMF generating cells. These cells are called electroplaques . It is discovered that a typical eel contains $140$ rows of $5000$ electroplaques, where each electroplaque is capable of generating an EMF of $0.15$ volts. The internal resistance of an electroplaque is approximately $0.25\ \Omega$ . If the water surrounding the eel has a resistance of $800\ \Omega$ , how strong is the maximum current (in Amperes) produced by the electric eel in the water?

This is my favourite circuits problem from Fundamentals of Physics by Halliday, Resnick, Walker.

Clarification: There are $140$ rows with $5000$ electroplaques, and each row is connected in parallel .

The answer is 0.927.

2 solutions

Chew-Seong Cheong
Aug 18, 2014

One roll of $5000\space \text{electroplaques}$ supply a voltage $V= 0.15V\times 5000 = 750V$ with a total internal resistance $R_{row}=0.25\Omega \times 5000 = 1250\Omega$ .

$140$ rows of $5000$ electroplaques still supply a voltage $V=750V$ but overall internal resistance is

$R=\cfrac{R_{row}}{140}=\cfrac{125}{14}=8.929\Omega$ .

The maximum current $I_{max}$ it can generate through surrounding water of $800\Omega$ is

$I_{max} =\cfrac{V}{R+800} =\cfrac{750}{808.929}= \boxed{0.927A}$

Why will the voltage of 140 rows remains the same?

Yash Chaudhary - 6 years, 3 months ago

We have to take rows as parallel connection.

Pulasthi Ekanayake - 5 years, 10 months ago

If that is the case the resistance also must be change it will divided per row

Venkatesh Rachabathuni - 5 years, 3 months ago

@Venkatesh Rachabathuni – The final equivalent circuit is a $750$ -V voltage source in series with an internal resistance of $8.929 \Omega$ and load of $800 \Omega$ .

Chew-Seong Cheong - 5 years, 3 months ago

I am adding a circuit diagram to explain it. Hope that it helps.

Chew-Seong Cheong - 3 years, 2 months ago

You can look at Millman's theorem

Basically you convert all the voltage sources to current sources, then calculate them and finally convert back to voltage source

Rifath Rahman - 2 years, 3 months ago

Of course, this is a simplified assumption to make calculation possible.

Chew-Seong Cheong - 5 years, 10 months ago

Kirchoff's voltage law for a parallel circuit,any of those circuits u take the total voltage of the whole setup will be sum of voltages of cell of any one row

neel Maiti - 5 years, 6 months ago

Can you tell me any good app for offline practice of questions

Akshay Tiwari - 4 years, 9 months ago

Select Electricity and Magnetism (or other topics) under Topics , you should find learning notes with examples and practise problems.

Chew-Seong Cheong - 4 years, 9 months ago

Why isn't resistance of surrounding water in parallel to the global resistance R of the eel?

Daniele Meli - 4 years, 4 months ago

The electrical resistance of surrounding water is very large compared to the internal resistance of 0.25 $\Omega$ and hence not included in the calculations.

Chew-Seong Cheong - 4 years, 4 months ago

I am adding a circuit diagram to explain it. Hope that it helps.

Chew-Seong Cheong - 3 years, 2 months ago

I see that geometrically it could seems they are in parallel, but actually they are not Try to think of it this way: two elements are in parallel if they are at the same potential and are in series if they carry the same current. In this case there's no reason to assume the water and the eel to be at the same potential but they are clearly run by the same current! I hope it helped!

Mario Roggi - 1 year, 2 months ago

i found it unclear what was parallel.. was it just the rows parallel to each other or the rows internally... (you should be able to get that form the question) ps: this Dutch electrician loves this site/app

Peter van Manen - 3 years, 9 months ago

I am adding a circuit diagram to explain it. Hope that it helps.

Chew-Seong Cheong - 3 years, 2 months ago

but 125/14 has indefinate digits!!! I did it then suddenly thought I've done something wrong and left. Thanks briliant for keeping it real instead of super simplifying school math.

Jason Anaminus - 3 years, 8 months ago

I am adding a circuit diagram to explain it. Hope that it helps.

Chew-Seong Cheong - 3 years, 2 months ago

I agree up to point: In each row all the 5000 electroplaques are connected in series,therefore equivalent emf=.15 x 5000=750V equivalent resistance of one series of electroplaques =0.15x5000=1250ohm. Now, Current develop by one series of electroplaques I = (V/R) = Voltage developed by one series of electroplaques / (Resistance of one series of electroplaques + Resistance of water connected in parallel) = 750 / (1250 in parallel to 800) = 750 / {(1250x800)/(1250+800)} = 750 / (1000000 / 2050) = 750 / 487.8 Current develop by one series of electroplaques = 1.5375 A Hence current developed by 140 no of (series of electroplaques) = 140 x 1.5375 A = 215.25 A. Please clarify the correction required.

Utkarsh Gaurav - 3 years, 2 months ago

I am adding a circuit diagram to explain it. Hope that it helps.

Chew-Seong Cheong - 3 years, 2 months ago

Omg u r clean

Robson Filho - 3 years ago

Shreya Sinha
Jan 27, 2018

In each row all the 5000 electroplaques are connected in series,therefore equivalent emf=.15 x 5000=750V equivalent resistance=0.15x5000=1250ohm all 140 rows are connected in parallel, equivalent resistance=1250/140=8.93 ohm thus resultant current in 800 ohm resistance =V/R=750/(800+8.93) A =0.927A

How an Electric Eel Stuns its Prey

The answer is 0.927.

2 solutions

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