Series Circuit Resistor Help: Solutions for Q1 and Q2

[MegaDeth]

Homework Statement

Here are pictures of the questions:

Q1:
http://i.imgur.com/3s9Ma.jpg


Q2:
http://i.imgur.com/0YChq.jpg

The Attempt at a Solution

Q1: As you can see, I have put down 1V above the 5V and 6V to the left. Is this right?

Q2: I have no idea what I've done.

 

[berkeman]

Homework Statement

Here are pictures of the questions:

Q1:
http://i.imgur.com/3s9Ma.jpg


Q2:
http://i.imgur.com/0YChq.jpg

The Attempt at a Solution

Q1: As you can see, I have put down 1V above the 5V and 6V to the left. Is this right?

Q2: I have no idea what I've done.

Sorry, the questions are not clear. What are you given, and what are you asked to find?

Also, you seem to show places where there are different voltages on the top and bottom of a pair of parallel connected resistors. If two resistors are in parallel, they will have the same voltage across them.

 

[MegaDeth]

Right, sorry, I though it was clear enough that I have to find the voltages that were unknown. If the voltages of two parallel resisters are the same, then in the first picture, there are two parallel resisters, so they'll be 5V each, does that mean that the one I filled in 6V should be 1V?

 

[berkeman]

Right, sorry, I though it was clear enough that I have to find the voltages that were unknown. If the voltages of two parallel resisters are the same, then in the first picture, there are two parallel resisters, so they'll be 5V each, does that mean that the one I filled in 6V should be 1V?

Do all the resistors have the same value of resistance?

 

[MegaDeth]

Yes they do.

 

[berkeman]

Right, sorry, I though it was clear enough that I have to find the voltages that were unknown. If the voltages of two parallel resisters are the same, then in the first picture, there are two parallel resisters, so they'll be 5V each, does that mean that the one I filled in 6V should be 1V?

Yes they do.

If they are all the same resistance value, and the configuration is one resistor in series with two parallel resistors, then you do not get 1V and 5V.

The total will add up to the 6V source voltage that you show, but the voltages across the resistors are not 1V and 5V.

What math are you using to calculate the voltage division?

BTW, the two circuits look the same to me. Are they supposed to be different configurations?

 

[MegaDeth]

Oh yeah, I just realized I had put a duplicate up. Here's the actual Q2:

http://i.imgur.com/nqPrY.jpg

Well, my teacher said that the total voltage of the circuit is equal to the voltages of the separate resisters added up.

 

[berkeman]

Oh yeah, I just realized I had put a duplicate up. Here's the actual Q2:

http://i.imgur.com/nqPrY.jpg

Well, my teacher said that the total voltage of the circuit is equal to the voltages of the separate resisters added up.

You are not getting the right answers for the resistor voltages. What equations are you using?

The fundamental equation is V=IR. The voltage across parallel components is the same. The current through series components is the same.

 

[MegaDeth]

We're only using V=IR, the question ask to complete the voltage readings on the voltmeters. Oh, it's D.C. by the way, if that changes anything. So basically, I know that the voltage changes in a series circuit but I'm not sure what the volt readings should be. Also if two resisters are in a parallel circuit but in an overall series circuit, they have the same voltage readings right? So how does the Q1 circuit work out?

 

[berkeman]

We're only using V=IR, the question ask to complete the voltage readings on the voltmeters. Oh, it's D.C. by the way, if that changes anything. So basically, I know that the voltage changes in a series circuit but I'm not sure what the volt readings should be. Also if two resisters are in a parallel circuit but in an overall series circuit, they have the same voltage readings right? So how does the Q1 circuit work out?

What is the overall resistance of two identical resistors in parallel?

 

[MegaDeth]

They're the same right?

 

[berkeman]

They're the same right?

I don't know what you mean by that statement.

If you put two 100 Ohm resistors in parallel, what is the resulting combined resistance?

 

[MegaDeth]

200 Ohm, but what I don't get is, if you look at the first picture, the voltages of 2 resisters in parallel are the same, the current changes. So, if I label one of the parallel resisters 5V, then is it right?

 

[berkeman]

200 Ohm, but what I don't get is, if you look at the first picture, the voltages of 2 resisters in parallel are the same, the current changes. So, if I label one of the parallel resisters 5V, then is it right?

No, not 200 Ohms. When you put resistors in series, their values add. So two 100 Ohm resistors in series make a total of 200 Ohms.

What do you get when you put two 100 Ohm resistors in parallel, and why?

 

[MegaDeth]

To be honest, I don't know, that's kind of why I'm asking. I really need to understand the answers to the questions I'm asking.

 

[berkeman]

To be honest, I don't know, that's kind of why I'm asking. I really need to understand the answers to the questions I'm asking.

It is strange that your teacher is not giving you the tools to figure out these questions.

Please read this introductory page at wikipedia:

http://en.wikipedia.org/wiki/Resistor

Now you should be able to tell us what the value of two parallel 100 Ohm resistors is...

 

[MegaDeth]

Ok, it's a 100 Ohms. Right, so will the voltage be the same as well?

 

[berkeman]

Ok, it's a 100 Ohms. Right, so will the voltage be the same as well?

No. Two 100 Ohm resistors in parallel do not still measure 100 Ohms.

What is the formula from the wikipedia page for the parallel combination of resistors? What do you get when you plug in 100 Ohms for the value of the two parallel resistors?

 

[MegaDeth]

Is it 1/Req = 1/R1 + 1/R2? If so, 1/Req = 1/100 + 1/100 which is 0.02.

 

[berkeman]

Is it 1/Req = 1/R1 + 1/R2? If so, 1/Req = 1/100 + 1/100 which is 0.02.

So if 1/Req = 0.2, what does Req equal?

And knowing what the parallel resistance is compared to the single resistor, what would you expect the voltage drops to be going around that circuit? They do need to add up to the total battery voltage applied, and the voltage drops will ratio with the effective resistances of each stage...

 

[MegaDeth]

50.

Sorry, but I can't really understand what you said. Are you talking about the circuit in the first picture?

 

[berkeman]

50.

Sorry, but I can't really understand what you said. Are you talking about the circuit in the first picture?

Sure, let's do the first circuit now. You have a 6V source, and then (going [STRIKE]clockwise[/STRIKE] counter-clockwise) you have a resistor (call it 100 Ohms), and then two parallel resistors (which you now know has a combined resistance of 50 Ohms).

So, since V=IR, what is the current that flows in the circuit? Remember that series resistances add, so the series combination of the 100 Ohm resistor and the 50 Ohm combined parallel resistors adds to what? So what is the current I then, since you have 6V across that total resistance?

Now you have the total I, so you can calculate the voltage drop across the 100 Ohm and 50 Ohm resistance.

Please show us your work and the solution for that first circuit. Then show us how you solve the 2nd circuit.

 

[MegaDeth]

The current that flows into the circuit is 0.06A. The series combination is 150 Ohms. The current is then 0.04A.

I'm not sure about this, but it she voltage drop:

0.06 x 100 = 6V - (0.04 x 50) = 2V

So is the voltage drop 4V?

 

[berkeman]

The current that flows into the circuit is 0.06A. The series combination is 150 Ohms. The current is then 0.04A.

I'm not sure about this, but it she voltage drop:

0.06 x 100 = 6V - (0.04 x 50) = 2V

So is the voltage drop 4V?

I don't know what the first sentence is about, but the rest is correct.

6V/150 Ohms = 0.04A = 40mA

So you get 4V dropping across the single 100 Ohm resistor, and 2V dropping across the two parallel resistors. That adds up to the total of 6V.

Now show us your work on the 2nd circuit. You're almost there!

 

[MegaDeth]

Single resistor = 100 Ohms
Parallel = 50 Ohm

Current = 9V / 250 = 0.036A

9V - ( 0.036 x 50) = 7.2V drop across first resistor.

7.2V - 1.8V = 5.4V drop across parallel resistors.

5.4V - 3.6V = 1.8V drop across the last resistor.

Hmm, I've gone wrong somewhere but I'm not sure where. Oh yeah, the actual question I asked was about what shall I fill in the voltmeter readings in the diagrams for the ones that I've filled in already, some of them are probably wrong but I'm not sure which ones. Basically what I had to do was fill in the voltmeter readings but I can figure them out.

 

[berkeman]

Single resistor = 100 Ohms
Parallel = 50 Ohm

Current = 9V / 250 = 0.036A

9V - ( 0.036 x 50) = 7.2V drop across first resistor.

7.2V - 1.8V = 5.4V drop across parallel resistors.

5.4V - 3.6V = 1.8V drop across the last resistor.

Hmm, I've gone wrong somewhere but I'm not sure where. Oh yeah, the actual question I asked was about what shall I fill in the voltmeter readings in the diagrams for the ones that I've filled in already, some of them are probably wrong but I'm not sure which ones. Basically what I had to do was fill in the voltmeter readings but I can figure them out.

You calculated the current correctly at 9V/250 Ohms = 36mA.

But after that, all you need to do to figure out the voltage drop across each resistor is to multiply the current and resistance, V=IR.

The current through each of the single 100 Ohm resistors is 36mA, so what voltage drop does that give you for each? And the current through the parallel resistors that have a total resistance of 50 Ohms is also 36mA, so what is the voltage drop across the parallel resistors? Do all 3 of those voltage drops add up to 9V?

 

[MegaDeth]

The voltage drop for the each 100 Ohm is 3.6V and for the parallel resistors, it's 1.8V. Oh yeah, that makes sense now. Ok, the second diagram is correct but what about the first one? should it be 5V for the other resistor which is part of the parallel section and 1V for the single resistor?

 

[berkeman]

The voltage drop for the each 100 Ohm is 3.6V and for the parallel resistors, it's 1.8V. Oh yeah, that makes sense now. Ok, the second diagram is correct but what about the first one? should it be 5V for the other resistor which is part of the parallel section and 1V for the single resistor?

We covered the first circuit in post #24.

 

[MegaDeth]

Yeah, but one of the parallel resistors had already been filled in as 5V.

 

[berkeman]

Yeah, but one of the parallel resistors had already been filled in as 5V.

Then the resistors are not of equal value. If they were, then the parallel combination of 2 resistors would always have half the resistance, so half the voltage drop. Having 3V across the single resistor and 2V drop across the parallel resistors is inconsistent with the assumption that all the resistors are equal in value.

You need to post the full text of the question, if you want further help.

 

[MegaDeth]

Right ok, all the question says is:

"For each of the following circuits complete the readings of the voltmeters."

If it's any help, it's related to Kirchoff's Second Law that in any closed loop, the sum of the p.d. across components in the loop is equal to the p.d. of the power supply.

 

[berkeman]

Right ok, all the question says is:

"For each of the following circuits complete the readings of the voltmeters."

If it's any help, it's related to Kirchoff's Second Law that in any closed loop, the sum of the p.d. across components in the loop is equal to the p.d. of the power supply.

Sigh.

Well, that's a completely different question then. The resistor values can be anything.

To fill in the blank voltmeter readings, you just remember that the voltage across parallel components is always the same, and like you said, the sum of the voltage drops and increases around a closed loop has to add to zero. You should be able to fill in the blank voltmeters now.