EMF and potential in a circuit

[Krushnaraj Pandya]

Homework Statement

Four identical cells each having emf E and internal resistance r are connected in series to form a loop abcd as shown in figure (picture 1). Find potential difference across ab and ac.

2. Homework Equations
V=IR
equations for combination of cells and resistances

The Attempt at a Solution

this is the circuit diagram-(picture 2. left for across ab and right one for across ac), I can find equivalent resistance easily, what confuses me is the sign of the emf- for ab three cells are sending current in one direction while one is in the opposite direction. So using +E for three and -E for one I get the answer -E/2 across ab but the correct answer is E/2. I think there's a fundamental mistake in my understanding of emf so I'd be grateful if someone can explain it to me in an simple, intuitive way. Thank you.

 

[tnich]

Homework Statement

Four identical cells each having emf E and internal resistance r are connected in series to form a loop abcd as shown in figure (picture 1). Find potential difference across ab and ac.

2. Homework Equations
V=IR
equations for combination of cells and resistances

The Attempt at a Solution

this is the circuit diagram-(picture 2. left for across ab and right one for across ac), I can find equivalent resistance easily, what confuses me is the sign of the emf- for ab three cells are sending current in one direction while one is in the opposite direction. So using +E for three and -E for one I get the answer -E/2 across ab but the correct answer is E/2. I think there's a fundamental mistake in my understanding of emf so I'd be grateful if someone can explain it to me in an simple, intuitive way. Thank you.

I think the only thing you are missing is the idea that you have to measure the EMF relative to a reference. If you measure the EMF at $b$ relative to $a$ you get one sign. If you measure the EMF at $a$ relative to $b$, you get the other sign.

 

[Krushnaraj Pandya]

I think the only thing you are missing is the idea that you have to measure the EMF relative to a reference. If you measure the EMF at $b$ relative to $a$ you get one sign. If you measure the EMF at $a$ relative to $b$, you get the other sign.

Got it after some thinking, thank you :D