How Does Electric Current Flow Through a Resistor in a Parallel Battery Circuit?

[Lindsayyyy]

Homework Statement

Two parallel connected batteries with internal electrical resistances R1 and R2 are connected with a resistance R of 5 ohm. Which electric current flows through R.

Homework Equations

U=I*R

U= voltage
R= resistance
I= electric current

The Attempt at a Solution

Hi everyone,

I have some trouble with this exercise as I'm fairly new to electrodynamics. The only idea I got so far was to sum the resistances as you do it when they are parallel connected:

1/R=1/R1+1/R2...

But then I have no idea how to go on. I could just calculate the R and insert it to the given formula I wrote down, but I'm far away from a specific answer to my question.
Can anyone give me some hints how I can solve this? Is there anything I'm missing?

Sorry for my bad english and for my lack of LaTex skill.

Thanks for your answers in advance.

Regards lindsayyyy

 

[gneill]

Does the attached figure match your circuit? Are the battery voltages, V1 and V2 equal?

Note that there are no parallel resistors in this circuit. There are two loops to solve using Kircchoff's voltage law, or if you prefer, a single node with three branches using the nodal method with branch currents.

 

[Lindsayyyy]

Thanks for your answer, your attached file looks like it should be. Sorry for forgetting a drawing of the problem.
The voltages are the same I guess, none are given at least.

edit: no parallel resistors? hm. Do I have to make a difference between inner resistors and the one with 5 ohm ? Am I not allowed to treach them as parallel ones?

 

[gneill]

Thanks for your answer, your attached file looks like it should be. Sorry for forgetting a drawing of the problem.
The voltages are the same I guess, none are given at least.

edit: no parallel resistors? hm. Do I have to make a difference between inner resistors and the one with 5 ohm ? Am I not allowed to treach them as parallel ones?

They are not parallel: none of the resistors are connected to each other at both ends.

You can write branch voltage equations for the three branches that connect at node A using the currents as indicated, and solve the resulting equations for the desired current, I3.

 

[rwisz]

Hi lindsayyyy,

Don't worry, we were all new to electrodynamics at some point! You are on the right track with summing the resistances in parallel, but you also need to take into account the voltage of each battery. The total voltage across the circuit can be found by adding the voltage of each battery (U1 and U2) and the voltage across the resistance (UR). This can be expressed as:

Utotal = U1 + U2 + UR

Then, using Ohm's law, we can rearrange the equation to solve for the current (I) as follows:

I = (Utotal - U1 - U2) / R

Since we know the values of U1, U2, and R, we can plug them in and solve for the current (I). I hope this helps! Keep practicing and you'll become more comfortable with these types of problems. Good luck!

Best,