electrical resistance

Stokoe10 · #1 $Old$ December 13th, 2008, 09:09 PM

could anyone help me with the following question.

appreciate any ones help.

The electrical resistance R of a wire of length l and cross-sectional area A (measured in m2) is given by the equation

R=pl/A
where ρ is a constant (known as resistivity) whose value depends on the metal used to make the wire. Note that Equation 1 is not introduced in S104 and you do not need to worry about the meaning of the symbols.
(i) Rearrange Equation 1 to make ρ the subject of the equation;
(ii) Use your answer to part (i) to find the units of ρ. You should express your answer in terms of the SI unit of resistance, and any other units in the answer should be SI base units (using letters and symbols to represent all units). Ensure that you show your working.

JD-Styles · #2 $Old$ December 13th, 2008, 11:22 PM

(i) To isolate p, multiply both sides of the equation by A, thus pl=RA, then divide by l, so p=RA/l

(ii) Resistence is measured in ohms ( $\Omega$ ) and the area is measured in square meters ( $m^2$ ), and l is measured in meters (m) so the units of p are $\Omega m^2/m= \Omega m$

Kiwi_Dave · #3 $Old$ December 14th, 2008, 12:40 AM

Quote:

Originally Posted by Stokoe10 $View Post$

could anyone help me with the following question.

appreciate any ones help.

The electrical resistance R of a wire of length l and cross-sectional area A (measured in m2) is given by the equation

R=pl/A
where ρ is a constant (known as resistivity) whose value depends on the metal used to make the wire. Note that Equation 1 is not introduced in S104 and you do not need to worry about the meaning of the symbols.
(i) Rearrange Equation 1 to make ρ the subject of the equation;
(ii) Use your answer to part (i) to find the units of ρ. You should express your answer in terms of the SI unit of resistance, and any other units in the answer should be SI base units (using letters and symbols to represent all units). Ensure that you show your working.

I don't know your background so please excuse me if you are more advanced than I have assumed.

Start with:

R=pl/A

Multiply both sides by A to get:

AR=pl

divide both sides by l to get:

$p=\frac{AR}l$

Now for part b, simply replace each symbol with the unit for that symbol to get:

unit for p = $\frac{m^2*Ohms}m$

Now simplify (cancel out a meters from top and bottom) to get your answer.