Question

A cylindrical conductor of length l and uniform area of cross section A has resistance R. Another conductor of length 2l and resistance R of the same material has area of cross section. 

A cylindrical conductor of length ‘l’ and uniform area of cross section ‘A’ has resistance ‘R’. The area of cross section of another conductor of same material and same resistance but of length ‘21’ is:

Options

• `"A"/2`

• `(3"A")/2 `

• 2A 

• 3A 

Answer 1

2A 

Explanation:

Let the resistivity of the material be ρ

Resistance (R) of the first cylindrical conductor = `(rho"l")/"A"`

where, l = length of conductor

A = area of cross section

Now, another cylindrical conductor has double length but same resistance. 

Let its area of cross section be A'

Its resistance (R') will be = `(rho xx 2"l")/"A"^"'"`

Since resistance is same

R = R'

`(rho xx "l")/"A" = (rho xx 2"l")/"A"^"'"`

Solving it, we get A' = 2A