Adding resistance and finding current in each branch

[nothing909]

Homework Statement

I have to calculate the current through each branch - I1, I2 and I3.

Homework Equations

The Attempt at a Solution

The only reason I'm having trouble with this problem is because the voltage source is in the middle and I'm a little confused. I am struggling even to add up the resistances.

Are the 2, 5, and 4Ω resistors in series with each other? Do I just add them all up to get the total resistance?

After I have the total resistance, I calculated the supply current (I2) by just using ohms law.

How is it I calculate I1 and I3? Is it current division?

 

[cnh1995]

You can use KVL in the two loops..

 

[nothing909]

You can use KVL in the two loops..

I forgot to mention that I'm doing superposition, I can't use KVL.

 

[nothing909]

I forgot to mention that I'm doing superposition, I can't use KVL.

 

[gneill]

The resistors are not in series. In fact you should be able to confirm quite easily that the 2 and 4 Ohm resistors are in parallel (they share the same potential difference as their leads are connected to the same two nodes). In fact, there are three parallel branches comprising the circuit. What does that tell you about the potential difference across all three? What relationship exists between the three branch currents (think KCL).

Draw in the currents:

Can you write KCL and KVL equations for the circuit?

 

[cnh1995]

I forgot to mention that I'm doing superposition, I can't use KVL.

For superposition, you need more than one sources.

 

[nothing909]

Yes, I had a 32V on the right, which I already dealt with. It's removed, now I'm left with the 18V source.

 

[gneill]

I forgot to mention that I'm doing superposition, I can't use KVL.

Sure you can. Superposition does not exclude the use of KVL or KCL. They are the basic circuit laws that you need to apply.

Superposition involves suppressing all but one source at a time and determining the circuit conditions, then summing the contributions from each of the individual sources. You can still invoke all the usual tools to find the individual contributions.

 

[cnh1995]

Yes, I had a 32V on the right, which I already dealt with. It's removed, now I'm left with the 18V source.

Use KCL and KVL. It is allowed in superposition( and in Thevenin and Norton too)..

 

[nothing909]

Sure you can. Superposition does not exclude the use of KVL or KCL. They are the basic circuit laws that you need to apply.

Superposition involves suppressing all but one source at a time and determining the circuit conditions, then summing the contributions from each of the individual sources. You can still invoke all the usual tools to find the individual contributions.

Is the total resistance for that circuit 6.3 ohms?

 

[cnh1995]

Is the total resistance for that circuit 6.3 ohms?

For KVL, it doesn't matter. But looking at the circuit, no two resistors are in series or in parallel.
Edit: 2 and 4 are in parallel..sorry! I drew it wrong..

 

[cnh1995]

Is the total resistance for that circuit 6.3 ohms?

6.33Ω, yes.

 

[nothing909]

For KVL, it doesn't matter. But looking at the circuit, no two resistors are in series or in parallel.
Edit: 2 and 4 are in parallel..sorry! I drew it wrong..

The first question I have on my question paper is:

Determine the current flowing through the 4 ohm resistor and the voltage drop across it using Kirchoff's laws, which I completed fine.

The next question is:

Determine the current flowing through the 4 ohm resistor and the voltage drop across it using superposition theorem.

Usually what I have is a circuit with two voltage sources. I remove one, calculate the total resistance and then the current in each branch.
I then remove the second voltage source and do the same thing - calculate the total resistance and then the current in each branch.

I then draw a matrix table thing to calculate the total current in each branch.

 

[cnh1995]

Usually what I have is a circuit with two voltage sources. I remove one, calculate the total resistance and then the current in each branch.
I then remove the second voltage source and do the same thing - calculate the total resistance and then the current in each branch.

That would be possible if there are series and parallel combinations of resistors(like this circuit). For complicated circuits, KVL and KCL work better.

 

[nothing909]

That would be possible if there are series and parallel combinations of resistors(like this circuit). For complicated circuits, KVL and KCL work better.

I calculated that the supply current (I2) is 2.86A. Is this correct? If so, how do I now go from that to calculating I1 and I3? Can I do current division or something?

 

[cnh1995]

I calculated that the supply current (I2) is 2.86A. Is this correct? If so, how do I now go from that to calculating I1 and I3? Can I do current division or something?

You can use current division since 2 ohm and 4 ohm are in parallel.

 

[nothing909]

You can use current division since 2 ohm and 4 ohm are in parallel.

So I3 = 0.953A and I1 = 1.906

Is that correct?

 

[cnh1995]

So I3 = 0.953A and I1 = 1.906

Is that correct?

Yes.

 

[nothing909]

Yes.

Okay, now I can do the matrix table thing and calculate the total current in each branch. I know where to go from here.

Thanks for your help.