physics practical question:-?

Question

why is the lenght of a wire used in metre bridge kept between 25 to 75?
A METRE BRIDGE is a device to measure the resistance of a given wire.

Answer 1

Hi, measuring the resistance is based on Ohm`s law, which is

U = R*I and R = U/I in V/A = Ohm

with U as the voltage drop in V over the resistance R in Ohm and I the current in A.

Now it depends from the device you are using. Basically yoü have to measure both the voltage drop and the current at the same time. Normally you will use direct votage around 6 V, which you can easily get by normal batteries. Then you need an ampmeter which can measure with sufficient accuracy currents in the range of some A.

Because an electrical wire has a resistance R of

R = l* rho/F with F = Pi*d^2/4

with l as the length of the wire, rho it`s specific resistance and F and d as the cross section respectively the diameter of the wire. It depends now from the diameter and the specific resistance rho of the wire material to come in the range of your ampmeter where it has the sufficient accuracy.

For example:

We take a cupper wire with a diameter of 0.1 mm and we want to use 6 V direct voltage. Cupper has an rho = 1,78*10^-8 Ohm*m or 0,0178 Ohm*mm^2/m.

Then we get from the above mentioned equations

l =Pi*d^2*U/(4*rho*I)

Calculating this equation leads to thje equation

l = 2,6/I in m

Using a current of 1 A would need a length l of 2,6 m. Using 3 A as a current you get 0,882 m and so on.

The result of all these thoughts is:

Because the easily available measuring devices are using commercial batteries and ampmeters for measuring currents in the range to 6 to 10 A the practical length of the wirte is in nthe range of parts of a meter.

If you would use only a short wire piece of 1 cm you would have to measure the current

I = Pi *U*d^2/(4*rho*I) = 264 A

This would be to much for two rfeasons:

1. The capacity of the used batteries is not large enough to maintain such a strong current for more than some ms.
2. Your ampmeter is normally not designed for such currents.

Answer 2

Actually the length of the metre bridge wire is 1m (100cm)
the calculations are done in between 25 - 75 to minimise end resistance which is the resistance due to the wire under the copper strips at the ends of the metre bridge. The metre bridge is most sensitive when the null point is found at the centre (i.e 50cm)

Answer 3

A shorter distance could cause too much current to flow through the bridge wire, possibly causing erroneous readings or damaging the device.

Answer 4

A shorter distance could cause too much current to flow through the bridge wire, possibly causing erroneous readings or damaging the device.

Answer 5

As current is inversely proportional to length, shorter distance could cause too much current to flow through the bridge wire, possibly causing erroneous readings or damaging the device.

Answer 6

Theoretically, you can have any length. It is not required to be within 25 and 75.