Current through resistor parallel to two different batteries

In summary, the conversation is about a circuit diagram with two batteries and a resistor. Using Kirchoff's Law, the current through the resistor is calculated to be 0.375 A, which is the correct answer. There may be a discrepancy with the answer key.
  • #1
Ellie
5
0

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.
 
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  • #2
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.
 
  • #3
Tanya Sharma said:
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.
 
  • #5




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!
 

FAQ: Current through resistor parallel to two different batteries

1. What is the formula for calculating current through a resistor in parallel to two different batteries?

The formula for calculating current through a resistor in parallel to two different batteries is I = (V1/R1) + (V2/R2), where I is the total current, V1 and V2 are the voltages of the two batteries, and R1 and R2 are the resistances of the resistor.

2. How do you determine the direction of current in a circuit with a resistor parallel to two different batteries?

The direction of current in a circuit with a resistor parallel to two different batteries can be determined by using Kirchhoff's current law. This law states that the total current entering a junction in a circuit must equal the total current leaving the junction. By applying this law to the parallel branches of the circuit, we can determine the direction of current flow.

3. What happens to the total current when you add a third battery in parallel to a circuit with a resistor parallel to two different batteries?

Adding a third battery in parallel to a circuit with a resistor parallel to two different batteries will increase the total current in the circuit. This is because the total voltage in the circuit will increase, leading to a higher current flow through the resistor.

4. How does changing the resistance of the resistor affect the total current in a circuit with two batteries in parallel?

Changing the resistance of the resistor will affect the total current in a circuit with two batteries in parallel. As the resistance increases, the total current will decrease, and vice versa. This is because the total current in a parallel circuit is inversely proportional to the total resistance in the circuit.

5. Can the current through a resistor in parallel to two different batteries ever be zero?

No, the current through a resistor in parallel to two different batteries can never be zero. This is because there will always be some voltage present in the circuit, even if it is very small, which will result in a non-zero current through the resistor.

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