Question

A tungsten wire has resistance R at 20°C. A second tungsten wire at 20°C has twice the length and half the cross-sectional area of the first wire. In terms of R, the resistance of the second wire is

Answer 1

Resistance will become 4 times of first wire resistance.

Step-by-step explanation:

At the temperature of both the the tungsten wire is same so we can apply ohm's law

Let the length of first wire is
`l_1` and cross sectional area is
`A_1`

Resistance of first wire
`R=(\rho l_1)/(A_1)`......1

Now length of second wire is twice the length of first wire

`l_2=2l_1` and cross sectional area
`A_2=(A_1)/(2)`.......2

Resistance of wire 2
`R_2=(\rho l_2)/(A_2)`........2

Dividing equation 1 by equation 1

`(R)/(R_2)=(\rho l_1)/(A_1)* (0.5A_1)/(\rho 2l_1)`

`R_2=4R`

Therefore resistance will become 4 times.