# Homework Help: Equation For Charging Current In Accumulator

1. Apr 14, 2012

### chikis

1. The problem statement, all variables and given/known data

Suppose we have a circuit represented, which is used for charging an accumulator from a.d.c supply of e.m.f, E1 and internal resistance, r1. If the e.m.f of the accumulator is E2 with an internal resistance of r2, then the equation for the charging current is what?
In this question, I want to know how to derive the equation for charging current in an accumulator.

2. Relevant equations

I know that there is equation that goes like this:
E = V + v
E = IR + ir
E = I(R + r)
I = E/(R + r)
But am not sure the above equation relates to my question in any way. Am optimistic that there are other equation that will be fit enough for this my questions.
3. The attempt at a solution

E = V + v
E = IR + ir
E = I(R + r)
I = E/(R + r)
but I don't think that this my working is correct or is fit for the question. Any help?

2. Apr 14, 2012

### Emilyjoint

I would say that the overall emf = E1-E2 and the total resistance - r1+r2.
So the current will be (E1-E2)/(r1+r2)
This checks out because when the battery is charged E2 = E1 and the current will then be zero

3. Apr 14, 2012

### chikis

Can you make the current, I the subject of the formular in any of the equation?

4. Apr 16, 2012

### chikis

Thank you so much. I understand from your reply that the current, I = (E1-E2)/(r1+r2)
But why is the overall emf = E1-E2? Can you give a principle that supports that?

5. Apr 16, 2012

### Staff: Mentor

Basically, voltages in series ADD. Here, you have one of opposite polarity to the other, in order to charge the accumulator correctly.

So, for a loop, the loop source voltage = the sum of the individual voltage sources