Resistivity Practical

Hi,
I am stuck on a resistivity practical. I am using the plotting of voltage against length to calculate the resistivity of a wire of Nichrome. I am unsure on a couple of points.

What is the precision reading of a: voltmeter ( 0-50V +/- 0.1V?!) , meter ruler & ammeter (0-100mA +/- 1 mA?!)

for possible errors i have mentioned zero starting errors but I am sure temperature is one as well but not sure what precautions I would use to keep the temperature the same also mentioned not putting the voltage too high as this would heat the wire.

As for the gradient ( 4 x I x Resistivity) / ( 4 x Diameter^2) Can someone please help me find the derivation for this from Resistivity = AR/l

Thanks

Reply 1

F1 fanatic

16

badeninc

Hi,
I am stuck on a resistivity practical. I am using the plotting of voltage against length to calculate the resistivity of a wire of Nichrome. I am unsure on a couple of points.

What is the precision reading of a: voltmeter ( 0-50V +/- 0.1V?!) , meter ruler & ammeter (0-100mA +/- 1 mA?!)

for possible errors i have mentioned zero starting errors but I am sure temperature is one as well but not sure what precautions I would use to keep the temperature the same also mentioned not putting the voltage too high as this would heat the wire.

As for the gradient ( 4 x I x Resistivity) / ( 4 x Diameter^2) Can someone please help me find the derivation for this from Resistivity = AR/l

Thanks

As a standard rule for precision the intrinsic error in any measuring device is half of the lowest value it can measure. So if it measures to 3 digits, say 100A then the error is 0.5A. Sometimes though, you may feel the error is worse than this and may want to add additional errors.

Precautions for temperature - doing all measurements on the same day/in the same room and some of them weren't in an oven/freezer.

Bit lost by what your "gradient" is. Where does the 4IR/4D^2 come from??

I would guess that you are plotting voltage against current, which is resistance, then use the gradient of your V-I graph (resistance) as R in the equation:

Resistivity = AR/L where you presumably know the diameter of you wire (area =pi*d^2) and the length.

Reply 2

badeninc

OP

2

No, I am plotting length against voltage . The gradient should give 4IR/4D^2 which i need to somehow fiddle with to get the resistivity in Ohm metres

Reply 3

F1 fanatic

16

badeninc

No, I am plotting length against voltage . The gradient should give 4IR/4D^2 which i need to somehow fiddle with to get the resistivity in Ohm metres

Ahh ok, well, V=IR and R=pL/A (being lazy, p is resistivity)

V/I = 4pL/(pi*d^2)

V=4pLI/(pi*d^2)

so the gradient is 4pI/(pi*d^2), from which you can work out the resistivity. No idea where the relation you have for gradient comes from, but the above formula seems to make more sense and gives you gradient in terms of resistivity if you re-arrange it.