How Can You Connect Four 5 Ohm Resistors for an Equivalent Resistance of 5 Ohms?

[paebo]

Guys I need your help about resistors...

These are the questions:
1. You have 4 identical resistors, each with resistance of 5 ohms. Show how you will connect the four resistors to get an equivalent resistance of 5 ohms.
(hint: there is more than one way)

2. As more doors are opened in a crowded room, the resistance to motion of people trying to leave the room is reduced. How is this similar to what happens when more branches are added to parallel circuit?

3. Are household circuits normally wired in series or in parallel? Why?

4. Biomedical Application. The parts of the body that are more sensitive to electric currents are the brain, the chest muscles, and the nerve centers that controls respiration and the heart. A current of 1 mA passing through the body will be barely noticeable, but a current of 80 mA will surely be fatal unless it is immeadiately stopped. In most situations, the amount of current that will flow into the body will depend on the condition of the skin at contact locations. Dry skin will have a high resistance but damp or wet skin will have low resistance. Why is this so?

Hope you can help me...

Thanks a lot

 

[cepheid]

This should be posted in the homework help section, and you should also post along with it what you have done so far in attempting the problems (we're not going to do your work for you. )

1. Hint: what is the equivalent resistance of two of the resistors connected in parallel?

2. Adding more branches is analogous to adding more doors to the room, because you have created more pathways for the current. This sentence is the key to the problem: "As more doors are opened in a crowded room, the resistance to motion of people trying to leave the room is reduced." Based on the analogy I noted above, can you rewrite the sentence so that it applies to the case of an electric circuit? I.e. can you fill in the result here:

As more branches are added to a parallel circuit, the resistance to __________________ is reduced.

3. Thinking about the answer to the "why?" question allows you to arrive immediately at the answer. Think about it this way...what happens if an element in a series circuit burns out? What about in a parallel circuit?

4. Here's a hint that gives away the answer!: Low resistance = high conductance. So...what can you tell me about wet skin, in that context?

 

[cyeokpeng]

To further add light to the last question, what do you know about the electrical characteristics of water? What is water made up of chemically?

The water molecules are highly polar, and hence there is a certain degree of ionization in the water molecules. Hence when a voltage is applied, some ions in the water will move in the direction of the applied electric field, and hence a small amount of current will flow. From this behaviour, we know that water has a relatively high conductance.

If the water has PH acidity, it will have even lower resistance due to higher concentration of ions present! That is the basic of the electroysis of water as two electrodes are placed in a slightly acidic water.

 

[paebo]

Nah, I can't seem to fin the answer for my 1st question... All I know is that combined resistance in parallel will always be less than any of the individual resistances... Help me sirs.

 

[cepheid]

All I know is that combined resistance in parallel will always be less than any of the individual resistances... Help me sirs.

Which is good, because you can see how that makes it possible to combine four 5 ohm resistors and yet still get an equivalent resistance of only 5 ohms. But you didn't work out the specifics...take a closer look at the hint I gave you:

What is the equivalent resistance of two of the resistors connected in parallel?

Just answer that question first, and then see if anything about it strikes you.

 

[paebo]

is it also two sir? hehe how dumb I am!

 

[cyeokpeng]

Mmm, what is the formula to find the equivalent resistance of two resistors in parallel?

R = ((1/R1)+(1/R2))^-1
=(R1*R2)/(R1 + R2)

So calculate yourself, the equivalent resistance of two 5 ohms resistors in parallel. I can tell you that your previous answer is wrong.

 

[Gokul43201]

is it also two sir? hehe how dumb I am!

paebo : besides guessing, what effort are you making to help yourself ?

 

[paebo]

Nah i solved it and is it 2.5? R= (1/5 + 1/5)^-1

 

[cepheid]

Yeah, you answered the question I posed to you. Now, answer me this:

If it is possible (as you have shown) to combine two 5 ohm resistors in parallel to get an equivalent resistance of 2.5 ohms, then can you see how to combine two sets of two 5 ohm resistors to get an equivalent resistance of 2.5 + 2.5 = 5 ohms?

 

[Ouabache]

4) Dry skin will have a high resistance but damp or wet skin will have low resistance. Why is this so?

To further add light to the last question, what do you know about the electrical characteristics of water? What is water made up of chemically?

The water molecules are highly polar, and hence there is a certain degree of ionization in the water molecules. Hence when a voltage is applied, some ions in the water will move in the direction of the applied electric field, and hence a small amount of current will flow. From this behaviour, we know that water has a relatively high conductance.

If the water has PH acidity, it will have even lower resistance due to higher concentration of ions present! That is the basic of the electroysis of water as two electrodes are placed in a slightly acidic water.

I see a lot of excellent hints and suggestions regarding this resistance thread.
We all appreciate that that cyeokpeng was trying to illustrate that water with ions present make it a better conductor than water alone or no water present.

However, he also mentioned some things that aren't true and would be misleading

It is true, water molecules are polar and due to inherent ionization, some ions will be present even in pure water; but only a small number of molecules (1 in 500 million) will ionize into hydrogen (H+) and hydroxide (OH-) ions. This does allow a small amount of current to flow. However it does not have a relatively high conductance. The conductance is on the order of 0.05 \muS/cm. (meaning a very high resistivity of 20 M\Omega). In fact a very low conductance.

However there are many impurities on the surface of the skin, one being salt which is naturally secreted in our sweat, this readily dissociates in water forming charged sodium (Na+) and chloride (Cl-) ions . Human sweat has an average concentration of 2.6 gm/L (2600 ppm) of salt ions equating to about 180 \Omega/cm making it Highly conductive!
Sweat is only slightly acidic (due to dissolved carbon-dioxide) and actually closer to neutral pH. In addition, sweat contains potassium, magnesium, calcium iron, copper, and zinc, all of which ionize in solution. It is all these electrolytes in solution that create a highly conductive skin surface.

Refs:
http://global.horiba.com/story_e/conductivity/conductivity_05.htm (conductivity of pure water)
http://www.firstendurance.com/electrolytes.html (concentration of salt in sweat)
http://www.omega.com/techref/ph-2.html (conductivity-to-resistivity conversion)

 

[cyeokpeng]

Hi,

Thanks for pointing out my mistakes. I really appreciate this, as in the process I can learn through my mistakes.

What you have said is actually more correct. I have remembered learning that pure water by itself is actually quite electrically insulating, because of the very small concentration of ions present.

So actually, it is the impurities on your hand that introduces the presence of ions dissociating in water that reduces the conductivity. Nice!

 

[Ouabache]

Yup, I'm here to learn as well. Glad to hear I didn't step on any
toes adding my 2 cents on the conductivity of water.

How is paebo making out with the resistance calculations?
Last I heard, he had two 5 \Omega resistors in combination to achieve 2.5 \Omega.. How about all 4 of them ?

Did paebo have any more thoughts on how the circuits are normally wired in the home?

 

[RhysticGenesis]

hmm as far as home goes thinking abnout it in diagram parallel would allow one post to switch off while allowing flow still to go through another allowing one appliance to turn off while keeping other on in one circuit compared to series where you knock out one you knock out the rest...