# Kirchoff's loop rule in a circuit with Many Cells in Parallel

My problem is that there are n cells connected in parallel, connected to an external resistor.

Now can we use Kirchoff's loop rule to evaluate the current through the resistor by considering a loop from the +ve terminal of a single cell to the -ve terminal of that cell?

If we do then wouldn't the equation be
$E-iR=0$
and $i$ will come out to be $E/R$? This implies that the current in resistor $R$ would remain constant even if a cell is removed. But superposition of current says it will be reduced.

• By "n cells" do you mean n identical voltage sources? – garyp Jul 23 '16 at 15:45
• Yep n identical Voltage sources – Shrish Dutta Jul 23 '16 at 15:47
• Understanding what you ask seems much harder as answering your question. But don't worry, simply give a lot of more info, maybe even your circuit diagram. – peterh Jul 23 '16 at 15:47
• In that case you are not applying Kirchoff's rules correctly. Work it out in detail for two cells. – garyp Jul 23 '16 at 15:49
• I added a picture, is my problem clear now? – Shrish Dutta Jul 23 '16 at 16:04

Your application of the Loop Rule is correct. The current around this loop is $i=E/R$.
However, although this is the only current going through that particular cell, it is not the only current going through the common resistor $R$. There are $n-1$ other loops through $n-1$ identical cells, each with the same loop current $i$. These loop currents are superposed, and add up to give the total current.
So after superposing all the loop currents, the current through each cell is $i=E/R$ and the total current through the common resistor is $ni=nE/R$.