How to determine terminal voltage for a circuit

[Strontium90]

Homework Statement

I am working on a direct current circuit and in the problem it has two power sources (batteries), three loads (resistances) and three circuit pathways. Two of the resistances are on the same path. The batteries are shown with their voltages in emf and not their terminal voltage values. I have tried a couple of times to determine the terminal voltages but to no avail. In the textbook that I am using it does not explain how to analyze a situation like this

Homework Equations

In this problem I am using Kirchhoff's rules to the circuit. I am also using the equation V = Ve - Ir for the Terminal Voltage and I = Ve / (R + r) for I in the Terminal Voltage Equation before.
This is the diagram of the problem that I am working on:

The Attempt at a Solution

The attempt has been to use Kirchhoff's rules to determine what "R" should equal in the equation for "I". This has resulted in numerous values of I that did not give the correct answer.

 

[collinsmark]

Homework Statement

I am working on a direct current circuit and in the problem it has two power sources (batteries), three loads (resistances) and three circuit pathways. Two of the resistances are on the same path. The batteries are shown with their voltages in emf and not their terminal voltage values. I have tried a couple of times to determine the terminal voltages but to no avail. In the textbook that I am using it does not explain how to analyze a situation like this

Substitute each battery with an an ideal voltage source and a resistor in series.

For example, the top path will contain an ideal 4 V voltage source, a 1 Ω resistor, and a 10 Ω resistor, all in series.

The bottom path will contain an ideal 8 V voltage source and a 1 Ω resistor, in series.

If you actually need to find the terminal voltage across a battery, it is the voltage of one side of the ideal voltage source relative to the other side of the corresponding resistor (the 1 Ω resistor that was added to the circuit). You will not be able to determine the terminal voltages until after you determined all the currents in the circuit. But you can use Kirchhoff's rules to find the currents.

[Edit: And welcome to Physics Forums!]

 

[cepheid]

Welcome to PF Strontium90!

Basically, you can model each battery as an ideal voltage source in series with a resistor representing the battery's internal resistance. If you do that, your circuit diagram ends up looking something like the diagram I've attached to this post.

If you apply KCL at the node that is circled in red, it tells you that:

I₃ = I₁ + I₂

with the currents being as I've labelled them in the diagram.

You also know that the voltage across each of the three branches in the circuit must be the same (because the three branches are in parallel).

This last fact gives you two equations that allow you to solve for your two unknowns (I₁ and I₂).

Once you know the currents in the branches with the batteries in them, you can figure out what the voltage drops across those batteries' internal resistors are.

EDIT: collinsmark beat me to it, but I hope that what I said (and the diagram) nicely complements what he said.

 

[Strontium90]

Hello everyone, sorry to respond so late. If I understand what you are saying, to get the value of cap R in the formula for the current for the terminal voltage, I follow the path from the negative terminal of the battery to the first resistance that I encounter, excluding the resistance of the battery itself? Is that correct? And thank you for your warm welcome to Physics Forums. I am impressed with the amount of activity and knowledge here.

 

[gneill]

The battery terminal voltage is the voltage "seen" across whatever internal parts comprise the battery. In this case it is an ideal voltage source and a specified internal resistance of one ohm. Draw a box around these parts and call it "battery".

 

[Strontium90]

Collinsmark I will not be able to figure out the currents of the circuits until I have the voltage of each pathway. From all of your responses I still do not understand how to resolve this problem. If I use the recommended values for determining the terminal voltages that you put in your post, I would get a value of 3.63 volts for the terminal voltage for the top path and a value of zero volts for the bottom path. I am missing something from what is being said in this discussion.

 

[gneill]

Replace the two battery symbols in the circuit diagram with a series combination of an ideal battery and a 1 Ω resistor. Now you have just a regular circuit to analyze; there are no unknown part values and nothing "odd" about any of the sources. Solve for the currents in each branch using whatever methods you need. These may include Kirchoff node, voltage, or current methods, or other methods if you've learned them. But you must analyze the circuit to determine the currents.

If it is this step that you are having trouble with, make an attempt and show us your work. We will try to help.

 

[Strontium90]

Hi Gneil, I worked out the problem in the way you recommended. The values I found for the currents relative to the resistors were close but not exactly to what the book had. I got a value of -0.924A for the 10 Ohm resistor while the book's answer is -0.935. For the 3 and 5 Ohm resistors, my value was 0.771 amps, while the book's answer was -0.785. Any idea why the minor discrepancy?

 

[gneill]

Hi Gneil, I worked out the problem in the way you recommended. The values I found for the currents relative to the resistors were close but not exactly to what the book had. I got a value of -0.924A for the 10 Ohm resistor while the book's answer is -0.935. For the 3 and 5 Ohm resistors, my value was 0.771 amps, while the book's answer was -0.785. Any idea why the minor discrepancy?

Are we looking at the same circuit? I don't see those values for currents. Perhaps you could share your calculations?