Circuits with two voltage sources

In summary: Kirchhoff's voltage law.) I1 and I2 are the currents that flow through the 4Ω and 10Ω resistors, respectively. These currents do not pass through the 2Ω resistor, so the voltage across that resistor is an intermediate result. (I1 and I2 are not intermediate results.) We need Vr to find I1 and I2. (And we need I1 and I2 to find the full current I = I1 + I2 that passes through the 2Ω resistor, since I = Vr/2Ω = (I1 + I2)/2Ω.)In summary, In this conversation,
  • #1
Chaso
23
0

Homework Statement



Well this is the problem:

Untitled_zpsb38107eb.png


Whats the current in I1 and I2?

Homework Equations


I'm guessing you use Kirthoff's Laws.

The Attempt at a Solution


Well, what I did was I broke it up to two different circuits but then it would have two different currents flowing into the 2 ohms resistor
 
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  • #2
Chaso said:

Homework Statement



Well this is the problem:

Untitled_zpsb38107eb.png


Whats the current in I1 and I2?

Homework Equations


I'm guessing you use Kirthoff's Laws.


The Attempt at a Solution


Well, what I did was I broke it up to two different circuits but then it would have two different currents flowing into the 2 ohms resistor

Hello Chaso, Welcome to Physics Forums.

Yes, Kirchhoff's laws are applicable. In addition, a handy technique for this type of circuit is superposition, which you may have covered in your coursework. You can consider the effects of one source at a time, suppressing all the others, then calculate their effects individually and sum together the results.

To "suppress" a voltage source you set its value to zero (replace the source with a wire). Then apply the usual circuit laws (Kirchhoff, Ohm, etc.) to solve for the parameters of interest (currents, potentials). Repeat for each source. Sum the results.
 
  • #3
So what I would do is just consider the current for the first half and than the other half and then I add the currents together for the 2 ohms resistor?
 
  • #4
Chaso said:
So what I would do is just consider the current for the first half and than the other half and then I add the currents together for the 2 ohms resistor?

That is essentially it. Remember, when you suppress a voltage source you effectively replace it with a wire. When you suppress the 2 V source, this puts its 10 Ω resistor in parallel with the 2 Ω resistor. Similarly, when you suppress the 3 V source the 4 Ω resistor will parallel the 2 Ω resistor.
 
  • #5
gneill said:
That is essentially it. Remember, when you suppress a voltage source you effectively replace it with a wire. When you suppress the 2 V source, this puts its 10 Ω resistor in parallel with the 2 Ω resistor. Similarly, when you suppress the 3 V source the 4 Ω resistor will parallel the 2 Ω resistor.

Ohhh. So I don't divide the circuits then I just take the current by replacing the voltages with a wire and do it for both voltage source and add up the current then?
 
  • #6
Chaso said:
Ohhh. So I don't divide the circuits then I just take the current by replacing the voltages with a wire and do it for both voltage source and add up the current then?

Yes.
 
  • #7
Hmm is there a method to check if the sums are correct? Like Kirthoff's Sum of Current law for a point. Do the sums add up to zero?
 
  • #8
Chaso said:
Hmm is there a method to check if the sums are correct? Like Kirthoff's Sum of Current law for a point. Do the sums add up to zero?

You can take your total current through the center resistor and use Ohm's law to determine the potential across it. Then with that potential in place you can find the potential drops across the other resistors (KVL around the individual loops), and hence the currents in those resistors. All the currents should satisfy KCL at the top center node.
 
  • #9
Well, I'm guessing that's what I did. I added up the I-total. that was 12/17.
and for the resistors:
2 ohm-10/17
4 ohm-19/34
10 ohm-9/34

and it doesn't seem to add up :/

But I got the I1 and I2 to be 10/17 and 18/17
 
  • #10
Chaso said:
Well, I'm guessing that's what I did. I added up the I-total. that was 12/17.
and for the resistors:
2 ohm-10/17
4 ohm-19/34
10 ohm-9/34

and it doesn't seem to add up :/

But I got the I1 and I2 to be 10/17 and 18/17

I'm not seeing the same numbers that you are, so one of us (or both) has a problem :smile:

Can you show more of your calculations of how you arrived at your results? Let's say the 2V supply is suppressed and only the 3V supply is operating. Can you show your work for finding the current through the 2Ω resistor?
 
  • #11
Well here's are all my numbers :).
HP0003_zps5ce8fbfe.jpg
 
Last edited:
  • #12
And I just added up the numbers to get the totals.
 
  • #13
Okay, so the currents through the 2Ω resistor due to the 3V source is (15/34)A, and due to the 2V source is (2/17)A, giving a total of Ir = (19/34)A . Note that both currents flow in the same direction, down through the 2Ω resistor, so they add. Adding the voltages produced across the resistor in a similar fashion yields Vr = (19/17)V across the 2Ω resistor.

With potential Vr across the resistor, for the full circuit the current I1 must be (3V - Vr)/4Ω. The current I2 is (Vr - 2V)/10Ω according to the current direction specified in the diagram. Do these expressions yield the results you've fond?
 
  • #14
gneill said:
Okay, so the currents through the 2Ω resistor due to the 3V source is (15/34)A, and due to the 2V source is (2/17)A, giving a total of Ir = (19/34)A . Note that both currents flow in the same direction, down through the 2Ω resistor, so they add. Adding the voltages produced across the resistor in a similar fashion yields Vr = (19/17)V across the 2Ω resistor.

With potential Vr across the resistor, for the full circuit the current I1 must be (3V - Vr)/4Ω. The current I2 is (Vr - 2V)/10Ω according to the current direction specified in the diagram. Do these expressions yield the results you've fond?

Hmm I'm kind of lost with the 2nd paragraph. I don't know what Vr is and how you are finding it and its connection with I1 and I2.
 
  • #15
Chaso said:
Hmm I'm kind of lost with the 2nd paragraph. I don't know what Vr is and how you are finding it and its connection with I1 and I2.

Vr is the net voltage across the 2Ω resistor; the sum (superposition) of the two voltages due to the two currents you found by suppressing the sources in turn. It's also equal to the voltage across that resistor due to the net current flowing through it.

Knowing the net voltage across the 2Ω resistor gives you the potential at the top center node. The individual currents I1 and I2 can then be calculated by considering the potential drops across the two other resistors.
 
  • #16
gneill said:
Vr is the net voltage across the 2Ω resistor; the sum (superposition) of the two voltages due to the two currents you found by suppressing the sources in turn. It's also equal to the voltage across that resistor due to the net current flowing through it.

Knowing the net voltage across the 2Ω resistor gives you the potential at the top center node. The individual currents I1 and I2 can then be calculated by considering the potential drops across the two other resistors.

Hmm okay so so Vr is universal to all the resistors then? That's why we find Vr with the 2Ω resistor and we can apply it to the other resistors? And to find the I in the 4Ω Resistor we subtract 3 by the Vr because 3 is flowing into it while Vr is flowing out and that's why its vice-versa for the 10Ω resistor?
 
  • #17
Vr is the potential across the 2Ω resistor in the complete circuit (with both voltage sources operating). So the top of the 2Ω resistor is at Vr above the ground potential. You can find the currents in the branches by doing a "KVL walk" from ground to the node where Vr sits. For example, for the left branch you have +3V - I1*(4Ω) = Vr. Solve for I1.
 
  • #18
gneill said:
Vr is the potential across the 2Ω resistor in the complete circuit (with both voltage sources operating). So the top of the 2Ω resistor is at Vr above the ground potential. You can find the currents in the branches by doing a "KVL walk" from ground to the node where Vr sits. For example, for the left branch you have +3V - I1*(4Ω) = Vr. Solve for I1.

So what I did was I1 = (3V - 19/17V)/4Ω = 8/17A

I2 = (19/17V - 2V)/10Ω = -3/34A

I'm assuming Vr is universal from 2Ω to 4Ω and 10Ω. If not, how would I find Vr for the other resistors? using the same method just add them up?
 
  • #19
Chaso said:
So what I did was I1 = (3V - 19/17V)/4Ω = 8/17A

I2 = (19/17V - 2V)/10Ω = -3/34A
Those currents look good.
I'm assuming Vr is universal from 2Ω to 4Ω and 10Ω. If not, how would I find Vr for the other resistors? using the same method just add them up?
Vr is the potential across the 2Ω resistor only. To find the others, use KVL since you know the potential at ground is 0 and that at the top node is Vr. The potential across the given resistor in the path must be such that it makes sum of potentials along the path equal this total. Another method is to use Ohm's law. If you know the current through the 4Ω resistor is I1, then the potential drop across it must be I1*4Ω.
 
  • #20
gneill said:
Those currents look good.

Vr is the potential across the 2Ω resistor only. To find the others, use KVL since you know the potential at ground is 0 and that at the top node is Vr. The potential across the given resistor in the path must be such that it makes sum of potentials along the path equal this total. Another method is to use Ohm's law. If you know the current through the 4Ω resistor is I1, then the potential drop across it must be I1*4Ω.

Hm okay that makes sense but why are we using Vr for the 2Ω to solve for the current of the other 2 resistors?
 
  • #21
Chaso said:
Hm okay that makes sense but why are we using Vr for the 2Ω to solve for the current of the other 2 resistors?

Well, rather than use the currents that you've already calculated, this provides a separate check on your results (you were looking for ways to check your results). You can also compare these currents with the the currents through these resistors found by superposition.
 
  • #22
Hmm okay that makes sense so how would I solve for I1 and I2 without Vr?
 
  • #23
Chaso said:
Hmm okay that makes sense so how would I solve for I1 and I2 without Vr?

Well, that's what you were doing before :smile:.

There are a number of circuit analysis techniques that can be applied. You chose superposition. You could also have applied source transformations, mesh analysis, or nodal analysis...
 
  • #24
Hmm okay thanks for the wonderful help. I think I got the hang of this now. Hmm quick question would a fan be equivalent to a resistor?
 
  • #25
Chaso said:
Hmm okay thanks for the wonderful help. I think I got the hang of this now. Hmm quick question would a fan be equivalent to a resistor?

A motorized fan? No, not really. It'll most likely look like a combination of resistance (small) and inductance. Is it a DC motor an AC motor?
 

1. How do you calculate the total voltage in a circuit with two voltage sources?

In a series circuit, the total voltage is equal to the sum of the individual voltages. In a parallel circuit, the total voltage is equal to the voltage of the highest voltage source.

2. Can two voltage sources with different voltages be connected in series?

Yes, two voltage sources with different voltages can be connected in series. However, the total voltage will be the sum of the individual voltages.

3. How does the direction of current change in a circuit with two voltage sources?

The direction of current in a series circuit with two voltage sources will be the same as the direction of the voltage sources. In a parallel circuit, the direction of current will depend on the voltage sources and the resistance of the circuit.

4. What happens if two voltage sources with the same voltage are connected in parallel?

If two voltage sources with the same voltage are connected in parallel, the total voltage will remain the same. However, the current will increase as the total resistance decreases.

5. Can a circuit with two voltage sources have a negative total voltage?

Yes, a circuit with two voltage sources can have a negative total voltage. This can happen when the voltages of the two sources are in opposite directions, causing the total voltage to be negative.

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