Current in a Circuit with Multiple Voltage Sources

[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!

 

[UltrafastPED]

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.

 

[berkeman]

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...

 

[CWatters]

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.

 

[dauto]

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

 

[sophiecentaur]

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.

 

[dauto]

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.

 

[LikesIntuition]

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!

 

[LikesIntuition]

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...

 

[sophiecentaur]

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