# Current in a Circuit with Multiple Voltage Sources

• LikesIntuition
In summary, the conversation discusses different techniques for solving DC circuit analysis problems and how they are based on Kirchoff's rules. The direction and magnitude of currents in a circuit can be determined by marking the diagram with arbitrary arrows and solving for the actual current. The Kirchoff rules are the basis for more sophisticated tools and are helpful in solving simple circuits before using these tools.
LikesIntuition
What exactly are the rules for conserving the currents in a circuit? If we have multiple emfs in parallel with each other, how can we figure out the direction and magnitude of currents in each segment of a circuit?

It makes perfect sense to me for one emf, and for the most part with two I can usually figure it out as well. So could we consider three emfs in parallel, and 3 resistors parallel to each other and each in series with the 3 emfs? In a set-up like this, how do we add up the currents? Do we do so arbitrarily?

I tried attaching an image, but am not sure if it worked.

Thanks for any help!

#### Attachments

• 20_82alt.gif
2.9 KB · Views: 663
There are several techniques which can be used to solve this type of problem:

1. Nodal analysis
2. Mesh current analysis
...
etc.

This lesson in DC circuit analysis covers the basics; Kirchoff's rules still apply, but you need a systematic approach in order to carry out the analysis correctly. These differing techniques work due to the linear nature of "ordinary" circuits which are based on passive components: resistors, capacitors, and inductors.

They also work for AC circuits, but then you use impedance.

LikesIntuition said:
What exactly are the rules for conserving the currents in a circuit? If we have multiple emfs in parallel with each other, how can we figure out the direction and magnitude of currents in each segment of a circuit?

It makes perfect sense to me for one emf, and for the most part with two I can usually figure it out as well. So could we consider three emfs in parallel, and 3 resistors parallel to each other and each in series with the 3 emfs? In a set-up like this, how do we add up the currents? Do we do so arbitrarily?

I tried attaching an image, but am not sure if it worked.
wahajwahajwahaj
Thanks for any help!

Multiple voltages sources cannot be paralleled unless they have the same voltage...

What exactly are the rules for conserving the currents in a circuit? If we have multiple emfs in parallel with each other, how can we figure out the direction and magnitude of currents in each segment of a circuit?

Regarding the direction...

Unless it's obvious the normal approach is to mark the diagram with arbitrary arrows which represent the direction you assume current will flow. Then solve the circuit equations to calculate the actual current. If the answer is negative that means current is flowing the other way.

For example see this circuit... Let's say I pretend I don't know which way the current will flow. To solve it I have arbitrarily chosen to define "Positive I" as flowing anticlockwise.

Applying KVL clockwise gives...

+10 + IR = 0

Note that it's "+IR" not "-IR" because if the current is flowing anticlockwise the bottom end of the resistor would be positive with respect to the top.

Rearranging this gives

I = -10/R

Oh look "I" has turned out to be negative. That means my assumption that the current was flowing anticlockwise was incorrect. In fact that's obvious in this example.

#### Attachments

• circuit.jpg
4.8 KB · Views: 459
LikesIntuition said:
What exactly are the rules for conserving the currents in a circuit? If we have multiple emfs in parallel with each other, how can we figure out the direction and magnitude of currents in each segment of a circuit?

It makes perfect sense to me for one emf, and for the most part with two I can usually figure it out as well. So could we consider three emfs in parallel, and 3 resistors parallel to each other and each in series with the 3 emfs? In a set-up like this, how do we add up the currents? Do we do so arbitrarily?

I tried attaching an image, but am not sure if it worked.

Thanks for any help!

Just use the Kirchhoff rules

dauto said:
Just use the Kirchhoff rules

HaHa
That's easy for you to say but for anything other than a simple circuit, the process can get very lumpy, very quickly.
But Kirchoff is the basis for the more sophisticated tools and it's well worth while using the two basic Kirchoff Laws for a simple circuit - to prove to yourself that they work. Then reach for the easier tools.

sophiecentaur said:
HaHa
That's easy for you to say but for anything other than a simple circuit, the process can get very lumpy, very quickly.
But Kirchoff is the basis for the more sophisticated tools and it's well worth while using the two basic Kirchoff Laws for a simple circuit - to prove to yourself that they work. Then reach for the easier tools.

Yes, but one hast to learn to walk before attempting to run The OP's example is quite simple which makes me think they might not be aware of the rules.

CWatters said:
Regarding the direction...

Unless it's obvious the normal approach is to mark the diagram with arbitrary arrows which represent the direction you assume current will flow. Then solve the circuit equations to calculate the actual current. If the answer is negative that means current is flowing the other way.

Thanks, that makes sense!

dauto said:
Yes, but one hast to learn to walk before attempting to run The OP's example is quite simple which makes me think they might not be aware of the rules.

You are correct. I'm pretty new to this stuff...

dauto said:
Yes, but one hast to learn to walk before attempting to run The OP's example is quite simple which makes me think they might not be aware of the rules.

I made that remark because I was thinking that the Kirchoff rules could be very scary, if the OP thought they were the only way to tackle all problems. I can't remember when I, personally have used K1 and K2 for any purpose other than to show they actually work. lol

## 1. What is current in a circuit with multiple voltage sources?

Current in a circuit with multiple voltage sources refers to the flow of electric charge through the circuit. It is measured in amperes (A) and is the rate at which electric charge passes through a given point in the circuit.

## 2. How is current affected by multiple voltage sources?

The current in a circuit with multiple voltage sources is affected by the sum of all the individual voltages in the circuit. The total current is determined by the combined effect of all the voltage sources and the resistance in the circuit.

## 3. What happens when voltage sources are connected in series?

When voltage sources are connected in series, their voltages add together. This means that the total voltage in the circuit is equal to the sum of all the individual voltages. The current remains the same throughout the circuit.

## 4. What happens when voltage sources are connected in parallel?

When voltage sources are connected in parallel, the current is divided between each source. This means that the total current in the circuit is equal to the sum of all the individual currents from each voltage source. The voltage remains the same across all branches of the circuit.

## 5. How do you calculate the total current in a circuit with multiple voltage sources?

To calculate the total current in a circuit with multiple voltage sources, you can use Ohm's Law (I=V/R) or Kirchhoff's Current Law, which states that the sum of all currents entering a node in a circuit must equal the sum of all currents leaving that node. You can also use the principle of superposition, which involves calculating the current for each voltage source separately and then adding them together to find the total current.

• Electromagnetism
Replies
3
Views
1K
• Electromagnetism
Replies
4
Views
1K
• Electromagnetism
Replies
8
Views
307
• Electromagnetism
Replies
1
Views
974
• Electromagnetism
Replies
6
Views
580
• Electromagnetism
Replies
5
Views
1K
• Electromagnetism
Replies
10
Views
1K
• Electromagnetism
Replies
16
Views
2K
• Electromagnetism
Replies
3
Views
2K
• Electromagnetism
Replies
21
Views
2K