What is the potential difference between points A and B in a circuit?

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SUMMARY

The potential difference between points A and B in a circuit with 2V and 4V electromotive forces (emfs) and internal resistances of 2Ω and 6Ω respectively is determined to be 0V, indicating a short circuit condition. According to Ohm's Law (V=IR) and Kirchhoff's Laws, when resistance approaches zero, the potential difference also approaches zero, confirming that the circuit behaves as a short circuit. If the calculated potential difference is anything other than zero, it indicates a problem in the circuit configuration.

PREREQUISITES
  • Understanding of Ohm's Law (V=IR)
  • Familiarity with Kirchhoff's Laws
  • Basic knowledge of circuit components (emfs and internal resistance)
  • Concept of short circuits in electrical circuits
NEXT STEPS
  • Study the implications of short circuits in electrical engineering
  • Learn about circuit analysis techniques using Kirchhoff's Laws
  • Explore advanced applications of Ohm's Law in complex circuits
  • Investigate methods for measuring potential difference in circuits
USEFUL FOR

Electrical engineering students, circuit designers, and anyone involved in analyzing or troubleshooting electrical circuits will benefit from this discussion.

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Homework Statement


The Cells in a circuit has 2V and 4V emfs and 2Ω and 6Ω internal resistance respectively. Find the potential difference between AB


Homework Equations


V=IR
Kirchoff's Laws


The Attempt at a Solution


The attempts are in image
 

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AB seems to be a shortcircuit. That is a potential difference of 0, so if you end up getting that, it's nothing to worry about. If you got something other than 0, that's when you should be worried. :wink:

Basically, you can think of a shortcircuit as taking a branch with a single resistor R, and doing R → 0. From V = IR, you see that I = V/R, so if R → 0, the only way to stop I from going to infinity and being a defined finite value, is to have V = 0, that is, the potential difference across a shortcircuit vanishes.
 
Metaleer said:
AB seems to be a shortcircuit. That is a potential difference of 0, so if you end up getting that, it's nothing to worry about. If you got something other than 0, that's when you should be worried. :wink:

Basically, you can think of a shortcircuit as taking a branch with a single resistor R, and doing R → 0. From V = IR, you see that I = V/R, so if R → 0, the only way to stop I from going to infinity and being a defined finite value, is to have V = 0, that is, the potential difference across a shortcircuit vanishes.
If VAB ≠ 0, then it would be I-i that goes to infinity.
 
The I in my explanation was the I of an arbitrary branch in which a shortcircuit is produced, I didn't use the same circuit as the one given. That's why I said V = IR, and not V = (I-i)R.

The I of my example would be extrapolated to whatever it need be, per particular circuit.
 
Ok thanks for help, i got it
 
You're welcome. :biggrin:
 

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