In short circuit condition, what is wrong with following derivation

In summary, the voltage V can be calculated using Ohm's law, V=ir, where V is the voltage, i is the current, and r is the resistance. However, this formula becomes V=E-ir when considering the whole circuit, where E is the voltage of the cell and ir is the voltage drop across the internal resistor. By substituting V with E-ir, we can then solve for i, which gives us i=E/2r. Finally, by substituting the value of i back into the original formula, V=E-ir, we get V=E/2, which is the voltage across the whole circuit. This analysis is based on the assumption that the load resistance is equal to the internal resistance.
  • #1
Theresa
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V=ir considering the whole circuit
Now we knowV=E-ir
Then ir=E-ir Therefore i=E/2r
Therefore,V=E/2
 
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  • #2
There is too much context missing. Where do you measure the voltage V? What is E? One of them seems to be used inconsistently.
Why is there a resistor if it's a short circuit?
 
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  • #3
Like @mfb said it's hard to help properly without further information, though I presume you're referring to a physical cell with internal resistance being shorted.

In that case, you're mixing up symbols. Your analysis as it stands is actually for a circuit with load resistance equal to the internal resistance.
 
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