Basic question regarding I=nAvq

Two pieces of wire A and B are made of the same material but have different diameters. They are connected in series with each other and a power supply.

(i) Which terms from the equation will be the same for both wires?
(ii) The diameter of A is twice that of B. Calculate the ratio vA:vB

For (i), I know it isn't A because A is area, and they have different areas so they also have different areas. However, I don't know which term it is.
Please can you help me?

(ii) I have no clue how to do this. Again, any help would be greatly appreciated.

Thanks!

Reply 1

Joinedup

20

resistors in series have the same current flowing through them... That's often useful to know

OP

Original post by Ravenous food

What? Can you help me please?

Reply 4

Joinedup

20

assume the wires are circular in cross section... what happens to the area of a circle if you double it's diameter?

Reply 5

Ravenous food

8

Original post by blobbybill

What? Can you help me please?

Reply 6

blobbybill

OP

11

Original post by Joinedup

assume the wires are circular in cross section... what happens to the area of a circle if you double it's diameter?

The area of the circle would double. I still don't get either of the questions though.

Reply 7

MRWAFFLE

3

Original post by blobbybill

The area of the circle would double. I still don't get either of the questions though.

I'm pretty sure the Area will be as of 4 times the initial one.
eg. A square with sides of 2cm. Area would be 4cm^2. If you double the length of the sides to 4cm, then the area would be 16cm^2.
Hope this helps!

Reply 8

Joinedup

20

Original post by blobbybill

The area of the circle would double. I still don't get either of the questions though.

+Mrwaffle is right...

also for circles where A=πr²

doubling the diameter also doubles the radius so the area goes up by a factor 4

this is interesting because the resistance of a wire depends on it's cross sectional area...
ρ=RA/l
ρ is a property of the material the wires are made of - and we're told they're made of the same material so ρ is the same for both.

ρ=RA/l
can be rearranged
R=ρl/A

so the wire that's got 1/4 the cross sectional area has 4 times more resistance for the same length.

Reply 9

blobbybill

OP

11

Original post by Joinedup

+Mrwaffle is right...

also for circles where A=πr²

doubling the diameter also doubles the radius so the area goes up by a factor 4

this is interesting because the resistance of a wire depends on it's cross sectional area...
ρ=RA/l
ρ is a property of the material the wires are made of - and we're told they're made of the same material so ρ is the same for both.

ρ=RA/l
can be rearranged
R=ρl/A

so the wire that's got 1/4 the cross sectional area has 4 times more resistance for the same length.

How do I do the question"The diameter of A is twice that of B. Calculate the radio vA:vB"? I think it means the v in the equation, so the drift velocity, but I don't get how to work out the answer to the question.

Thanks

Reply 10

Joinedup

20

Original post by blobbybill

How do I do the question"The diameter of A is twice that of B. Calculate the radio vA:vB"? I think it means the v in the equation, so the drift velocity, but I don't get how to work out the answer to the question.

Thanks

OK so the current is the same in both pieces of wire because they're in series... I is the same for both.
n is a property of the material the wires are made of - and they're both made of the same material so n is the same for both wires.
q is the charge per charge carrier - in metal wires the charge carrier is the electron and an electron in wire A carries the same charge as an electron in wire B

A (area) is different for the 2 wires

The formula says I=nAvq, if one of the wires has A 4 times larger than the other... and the only other variable that's able to change is v... what has to happen to v to keep I the same?

Basic question regarding I=nAvq

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