Question

One wire has a cross-sectional area of 1,250 cmil and a resistance of 7 ohms. A second piece of wire, identical except for cross-sectional area, has a resistance of 10 ohms. Determine what the cross-sectional area of this second wire is. (Cross-sectional area and resistance are inversely proportional.)

Answer 1

Answer:

875 cmil

Explanation:

Cross section area of wire=$A_1=1250 cmil$

Resistance of wire,$R_1=7\Omega$

$R_2=10\Omega$

We have to find the cross sectional area of second wire

We know that

$R=\frac{\rho l}{A}$

According to question

$l_1=l_2=l,\rho_1=\rho_2=\rho$

$R_1=\frac{\rho l}{1250}$

$7=\frac{\rho l}{1250}$....(1)

$10=\frac{\rho l}{A}$...(2)

Equation (1) divided by equation (2) then, we get

$\frac{7}{10}=\frac{A}{1250}$

$A=\frac{7}{10}\times 1250=875cmil$

Hence, the cross- sectional area of second wire=875 cmil