Circuit with 2 batteries is confusing me

[mujadeo]

Homework Statement

The circuit in the figure is composed of two batteries (E1 = 6 V and E2 = 4 V) and three resistors (R1 = 4 , R2 = 4 , R3 = 5 ) as shown.

(a) What is the current I3 flowing through the batteries?

I3 = .286A (no problem here)

(b) What is the voltage Vb - Va between the points a and b in the circuit?

Vb - Va = V

So i combined the parallel Rs to get R1 + R2 = 2ohms
So voltage in is 2V right?
Then voltage on other side of Req should be .579V right? (because I=.286A)
so then 2V - .579V = 1.43 = wrong answer
please help!

thanks

Homework Equations

The Attempt at a Solution

 

[Doc Al]

(b) What is the voltage Vb - Va between the points a and b in the circuit?

Vb - Va = V

So i combined the parallel Rs to get R1 + R2 = 2ohms

Good.

So voltage in is 2V right?

How did you deduce this? You have the resistance and the current.

Then voltage on other side of Req should be .579V right? (because I=.286A)

Do you mean the voltage across R3? What's the current through R3?

 

[mujadeo]

because picture says current is going cw, so 1st batt is -4V and 2nd batt is 6V = 2V
so 2V enters Req.
Req = 2ohms
and total current in the circuit is .286A
so V=IR = .286 X 2ohm = .579V
2V - .579V = 1.421V

 

[Doc Al]

Much better. (Unless the reference point is very clear, it's always a good idea to specify the voltage difference between two points or across something.)

 

[mujadeo]

1.421V is wrong answer though, so can u please tell me what I am doing wrong?
thanks

 

[Doc Al]

You did the work correctly, but you're getting confused about which voltage drop is the answer to the question.

because picture says current is going cw, so 1st batt is -4V and 2nd batt is 6V = 2V
so 2V enters Req.
Req = 2ohms

This is the equivalent resistance between points A and B.

and total current in the circuit is .286A

This is the total current going through both R3 and between points A and B.

so V=IR = .286 X 2ohm = .579V

That's the voltage drop across A and B. That's the answer to the question.

2V - .579V = 1.421V

That's the voltage across R3.