Current through resistor parallel to two different batteries

[Ellie]

Homework Statement

I'm sorry that I have no pic, but please bear with my description.

The circuit diagram is made up of 3 horizontal lines. On the top line, there's battery A, (-) on the left, (+) on the right, and an arrow going to the right (>) to show direction of current.

On the middle line, there's the 2 Ω resistor.

And on the bottom line, there's battery B, (+) on left, and (-) on right.

Battery A has an e.m.f, of 2.0 V and an internal resistance of 1 Ω. For battery B, the values are 1.0 V and 2 Ω. A and B are connected to a 2 Ω resistor. Using Kirchoff's Law, calculate current through the resistor.

Homework Equations

Both of Kirchoff's Law.
I1 = I2 + I3
E = IR1 + IR2

The Attempt at a Solution

I tried taking the top and middle, and treated it as one circuit, and did the same with the middle and bottom. Then I applied Kirchoff's second law. In this way, I managed to get two equations with three different variables.

2 * I3 + I1 = 2
- 2 * I3 + 2 * I2 = 1

Where I1 is the current leaving battery A, I3 is the current entering the middle section after entering a junction, and I2 is the other current going toward the bottom section.

Then by using I = I1 + I2 + I3, as well as the two equations, I substituted the values around, until I managed to make the equation in terms of I3.

The value I got is 0.375 A.

The answer is supposed to be 0.42 A.

It would be great if someone can point out where I did wrong.

 

[Tanya Sharma]

Welcome to PF !

As per the circuit description you have given , 0.375 A is the correct answer . So I think you have got it right .

Either the answer key is wrong or the original question description is somewhat different from what you have given.

 

[Ellie]

Welcome to PF !

As per the circuit description you have given , 0.375 A is the correct answer . So I think you have got it right .

Either the answer key is wrong or the original question description is somewhat different from what you have given.

Thank you for clarifying. I'll see if I've misunderstood somewhere.

 

[rude man]

Tanya has it right.

 

[HalfLostAndSearching]

Your approach to solving this problem using Kirchoff's Laws is correct. However, there may have been a mistake in your algebraic manipulations. It would be helpful if you could show your work in more detail, so that we can identify where the error may have occurred. Additionally, it is always a good idea to double check your calculations to ensure accuracy. In this case, the correct answer is indeed 0.42 A, so it is possible that there was a small error in your calculations. Keep up the good work in applying Kirchoff's Laws to solve circuit problems!