# Circuits with Series and Parallel Wiring

#### Snape1830

I attached the problem. I'm pretty confused. I remember the equations for parallel and series circuits, but I have no idea how to do this. I attempted, but failed. I know the two 10 ohm resistors are in parallel (so Rnet is 5), and the 20 ohm and the 6 ohm resistor are in series (So Rnet is 26). But then are those in parallel or series? And then i just don't know how to do the problem.

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#### vela

Staff Emeritus
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The 10-ohm resistors are in parallel, but the 20-ohm and 6-ohm resistor aren't in series.

#### Snape1830

The 10-ohm resistors are in parallel, but the 20-ohm and 6-ohm resistor aren't in series.
Is the 10, 10 and 20 ohm in parallel and the 6 ohm in series with those three? Otherwise, I can't see how the 20 and the 6 aren't in series.

#### vela

Staff Emeritus
Homework Helper
The 20-ohm and 6-ohm are not in series because there's something else connected to the node where the two resistors are connected. If two elements are in series, all of the current in one element has to go through the other element. For example, the battery and the 6-ohm resistor are in series. You should be able to see that all of the current that flows through the battery has to also go through the 6-ohm resistor. That's not the case with the 6-ohm and 20-ohm resistor. Some of the current that goes through the 6-ohm resistor will branch off to go through the 10-ohm resistors.

#### Snape1830

The 20-ohm and 6-ohm are not in series because there's something else connected to the node where the two resistors are connected. If two elements are in series, all of the current in one element has to go through the other element. For example, the battery and the 6-ohm resistor are in series. You should be able to see that all of the current that flows through the battery has to also go through the 6-ohm resistor. That's not the case with the 6-ohm and 20-ohm resistor. Some of the current that goes through the 6-ohm resistor will branch off to go through the 10-ohm resistors.
Ok....so how do I do the problem?

#### mrcheeses

10 ohm resistors aren't in a series and are parallel but the other two are in a series. I find it easy to see if they are parallel or series by redrawing the diagram to one you are comfortable with. At every split in the wire with resistors, just branch it off.

#### Snape1830

10 ohm resistors aren't in a series and are parallel but the other two are in a series. I find it easy to see if they are parallel or series by redrawing the diagram to one you are comfortable with. At every split in the wire with resistors, just branch it off.
So 20 and 6 are in series? That's what I thought. I'm not really sure how to redraw it. Can you can just help me get the answer?

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#### ehild

Homework Helper
I redraw the circuit making the wires a bit shorter and moving the ammeter closer to the resistors, but the circuit is equivalent with the original one. Note that the ammeter can be replaced by a single piece of wire. Which resistors are connected in parallel?

ehild

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#### azizlwl

Yes, 10,10 and 20 ohms are in parallel.

#### Snape1830

I redraw the circuit making the wires a bit shorter and moving the ammeter closer to the resistors, but the circuit is equivalent with the original one. Note that the ammeter can be replaced by a single piece of wire. Which resistors are connected in parallel?

ehild
10, 10 and the 20 ohm resistor are in parallel. So the Rnet is 4 for those? So then do I just use V=RI to solve for current?

#### ehild

Homework Helper
Yes, the resultant of the parallel resistor is 4 ohm. And the resultant is connected to the 6 ohm resistor, and the whole is connected to the battery. You can use V=RI to get the total current.

What current does the ammeter read?

#### Snape1830

Yes, the resultant of the parallel resistor is 4 ohm. And the resultant is connected to the 6 ohm resistor, and the whole is connected to the battery. You can use V=RI to get the total current.

What current does the ammeter read?
Well, 4+6=10.
So...
20=10I
I=2 A

But 2 is wrong, so I don't know.

#### ehild

Homework Helper
The ammeter does not read the current flowing through the battery. It reads the current that flows through itself. It is connected in series with what ?

ehild

#### Snape1830

The ammeter does not read the current flowing through the battery. It reads the current that flows through itself. It is connected in series with what ?

ehild
The three resistors in parallel? But to find current you need to know the voltage.

#### ehild

Homework Helper
The three resistors in parallel? But to find current you need to know the voltage.
No it is not the three resistors in parallel, but?
And you can find the voltage.

ehild

#### Snape1830

No it is not the three resistors in parallel, but?
And you can find the voltage.

ehild
Just the two 10s? How do I find the voltage if I only have the resistors?

#### azizlwl

Well, 4+6=10.
So...
20=10I
I=2 A

But 2 is wrong, so I don't know.
Now you got 2 Amps flowing through the equilvalent parallel resistors and through 6 Ohms resistor.

Now what is the voltage across each of the parallel resistors?
From this voltage drop, you calculate the current flow.

What is required here is to find the current flowing through the equivalent parallel resistors of two 10 Ohms resistors.

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#### Snape1830

Now you got 2 Amps flowing through the equilvalent parallel resistors and through 6 Ohms resistor.

Now what is the voltage across each of the parallel resistors?
From this voltage drop, you calculate the current flow.
V-RI
V=10(2)
V=20 V
V=20(2)
V=40 V

So across the 10 ohm resistors, the voltage drop is 20 V
Across the 20 ohm resistor the voltage drop is 40 V?

That 40 can't be right, though?

#### azizlwl

Wrong.
With equivalent parallel resistors, you have only 2 resistors. 6 ohms and 4 ohms.
What is the voltage drop across 4 ohms resistor.
This voltage drop is identical to all the resistors in parallel.
Remember the voltage across all resistore in parallel are equal.

#### Snape1830

Wrong.
With equivalent parallel resistors, you have only 2 resistors. 6 ohms and 4 ohms.
What is the voltage drop across 4 ohms resistor.
This voltage drop is identical to all the resistors in parallel.
Remember the voltage across all resistore in parallel are equal.
Oh, right, I misread the question.
V=2(4)
V=8 Volts

#### ehild

Homework Helper
Oh, right, I misread the question.
V=2(4)
V=8 Volts
So the voltage across the resultant of the parallel resistors is 8 V. You get the current through each of them if you divide that 8 V by the resistances.
What is the current that flows through the ammeter?
Remember Kirchhoff's nodal law.

ehild

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#### Snape1830

So the voltage across the resultant of the parallel resistors is 8 V. You get the current through each of them if you divide that 8 V by the resistances.
What is the current that flows through the ammeter?
Remember Kirchhoff's nodal law.

ehild
Kirchoff's loop rule? The current going in equals the current coming out.
So do I find the current through of the parallel resistors and then add them up...because that comes out to 2 and 2 is wrong.

#### ehild

Homework Helper
Kirchoff's loop rule? The current going in equals the current coming out.
So do I find the current through of the parallel resistors and then add them up...because that comes out to 2 and 2 is wrong.
I wrote Kirchhoff's node rule.

The ammeter measures the current that flows through it. Does I20 ,represented by the green arrow flow through the ammeter?

ehild

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#### Snape1830

Wrote Kirchhoff's node rule.

The ammeter measures the current that flows through it. Does I20 ,represented by the green arrow flow through the ammeter?

ehild
No? So it would be 1.6 A?

And thanks for taking the time to edit the picture!

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