Question

Electric eels and electric fish generate large potential differences that are used to stun enemies and prey. These potentials are produced by cells that each can generate 0.10 V. We can plausibly model such cells as charged capacitors.

(a) How should these cells be connected (in series or in parallel) to produce a total potential of more than 0.10 V? (b) Using the connection in part

(a), how many cells must be connected together to produce the 500-V surge of the electric eel?

Short answer

(a) To produce a total potential of more than 0.10V, the cells must be connected in series.

(b) The number of cells is 5000 to be connected together to produce the 500-V surge of the electric eel.

Step-by-step solution

About Potential

We are given the potential produced by each cell $V=0.10V$. Where the electric fish generates large potential differences that are used to stun enemies.

(a) In a parallel connection the potential difference for all individual capacitors is the same and is equal to

$V_{total}=V$

Where V is the potential of each cell. While in a series connection the potential differences of the individual capacitors are not the same unless their individual capacitances are the same and the potential differences of the individual capacitors add to give the total potential difference as next

$V_{total}=V_1+V_2+V_3+....$

Where the total potential is higher than the individual capacitors

Hence, to produce a total potential of more than 0.10 V, the cells must be connected in series.

Number of cells

(b) The cell connection is in series so to produce $V_{total}=V$and as each cell has the same potential then equation (1) will be in the form

$V_{\text{total}}=NV$

Where is$V_{\text{total}}$ the total potential difference, N is the number of cells.

$N=\frac{V_{t\text{otal}}}{V}$

Substitute the 500 V for V_total, and 0.1 V for V in the above equation

$\begin{array}{rcl}N& =& \frac{\text{500}\text{V}}{\text{0.1}\text{V}}\\ & =& 5000\end{array}$

Thus, the number of cells is 5000 to be connected together to produce the 500-V surge of the electric eel.