what happens with the resistance of a wire with twice the diameterby koat Tags: diameter, resistance, wire 

#1
Nov1610, 12:52 PM

P: 40

hi everybody
Question: a length of uniform wire has a R of 2 ohms. calculate the R of a wire of the same metal and original length but twice the diameter. I thought as the wire gets twice as thick the R must halve to 1ohms. But the solution is 0.5 ohms. what did i do wrong? thanks in advance 



#2
Nov1610, 12:56 PM

Emeritus
Sci Advisor
PF Gold
P: 5,198

Can you list for me the parameters that resistance depends upon? (Hint: it does not depend *directly* on the diameter.) Which one of these parameters is relevant here?




#3
Nov1610, 01:00 PM

P: 40

is it that the R decreases when the A increases?




#4
Nov1610, 01:03 PM

Emeritus
Sci Advisor
PF Gold
P: 5,198

what happens with the resistance of a wire with twice the diameter
Yes, crosssectional area is one of the parameters on which resistance depends. (I had asked you to list all of the parameters, but this one is the relevant one here). So, what does changing the diameter do to the area? What does that resulting change in area do to the resistance?




#5
Nov1610, 01:06 PM

P: 40

is it that when you double the diameter you double the A?




#6
Nov1610, 01:08 PM

P: 40

as the area increases the R decrease




#7
Nov1610, 01:09 PM

Emeritus
Sci Advisor
PF Gold
P: 5,198





#8
Nov1610, 01:11 PM

P: 40

r ^2 times pi




#9
Nov1610, 01:17 PM

Emeritus
Sci Advisor
PF Gold
P: 5,198





#10
Nov1610, 01:20 PM

P: 40

sorry i don't get what you mean with the A depends on the square of diameter.
can you show me an example with numbers please so that i can visualise this problem? 



#11
Nov1610, 01:33 PM

Emeritus
Sci Advisor
PF Gold
P: 5,198

Alright look. Let's call the original diameter d_{1}. Now:
[tex] A_1 = \pi r_1^2 [/tex] But the radius is just half the diameter, so: [tex] r_1 = d_1 / 2 [/tex] Agreed? Therefore: [tex] A_1 = \pi \left(\frac{d_1}{2}\right)^2 = \pi \frac{d_1^2}{4} [/tex] This is how the area of a circle depends upon its diameter. As you can see, area is equal to a constant times the diameter squared. Now, what happens if we change the diameter by doubling it? Let's call the new diameter d_{2} so that: [tex] d_2 = 2d_1 [/tex] We can plug this new diameter into the formula for the area in order to find the new area: [tex] A_2 = \pi \frac{d_2^2}{4} = \pi \frac{(2d_1)^2}{4} = 4 \pi \frac{d_1^2}{4} = 4A_1 [/tex] So we have the result that A_{2} = 4A_{1}. After doubling the diameter, the new area is equal to FOUR times the original area. This is because the area of a circle is proportional to its diameter SQUARED. So if you double the diameter, you quadruple the area. If you triple the diameter, you increase the area by a factor of nine. If you quadruple the diameter, the area increases by a factor of 16. Now do you understand? 



#12
Nov1610, 01:42 PM

P: 40

wow I'm impressed with that.
Yes I understand now. Thanks a lot for your answer :) 


Register to reply 
Related Discussions  
finding length and diameter of wire  Introductory Physics Homework  1  
Diameter of a wire with length, resistance and resistivity  Advanced Physics Homework  2  
What diameter wire should be used for particular resistance?  Introductory Physics Homework  1  
Diameter of a wire  Introductory Physics Homework  4  
Fabricate uniform wire out of 2.1g of copper w/ 0.3 ohm resist.  wire diameter?  Introductory Physics Homework  2 