Answer:
Ok, is this your homework? Just 2 very simple formulae, which you should know, then plugging in some numbers & calculating the result.
So, bear with me…
Resistance = rho x l/a …(p)
Where l is length in meters, a is area in square meters & rho is resistivity in ohm meters.
Resistivity is a bulk property of the material, and for silver, at 20 degrees C, is given in tables as 1.59 exp -8 [1.59 times 10 to the minus 8th power]
So, for formula (p), we know rho, as above; length is 2m, R is 0.5 ohm, and we want to find area, from which we can calculate diameter.
Rearranging (p), we get a = (rho x l)/R
So a = (1.59 exp -8 x 2)/0.5
Multiplying top & bottom of the fraction by 2 gives
a = 6.36 exp -8
So the cross sectional Area of the wire is 6.36 exp -8 square meters.
Since the question asks for a diameter, we assume the wire is circular in section. You should know that the are of a circle is given by Pi x radius squared…
A = Pi x r^2 (q)
Rearranging (q) to find radius gives
r = square root of (A/Pi)
So the radius of the wire is SQRT (6.36 exp -8/Pi) which is SQRT of approx 2.0445 exp -8
This calculates to approx 1.42283 exp -4
The diameter is of course twice the radius, so approx 2.84566 exp -4
Let's say about 2.85 exp -4 meters
This is 0.285 millimeters
So rather more than human hair thickness. It is roughly equivalent to 29 AWG wire.
Got it?
Step-by-step explanation:
Material Electrical Resistivity at 20°C Ohm metres
Silver 1.6 x 10-8
Tantalum 1.3 x 10-7
Tin 1.1 x 10-7
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