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

875 cmil

Step-by-step 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=(\rho l)/(A)`

According to question

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

`R_1=(\rho l)/(1250)`

`7=(\rho l)/(1250)`....(1)

`10=(\rho l)/(A)`...(2)

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

`(7)/(10)=(A)/(1250)`

`A=(7)/(10)* 1250=875cmil`

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