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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

Respuesta :

Answer:

Resistance will become 4 times of first wire resistance.

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 [tex]l_1[/tex] and cross sectional area is [tex]A_1[/tex]

Resistance of first wire [tex]R=\frac{\rho l_1}{A_1}[/tex]......1

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

[tex]l_2=2l_1[/tex] and cross sectional area [tex]A_2=\frac{A_1}{2}[/tex].......2

Resistance of wire 2 [tex]R_2=\frac{\rho l_2}{A_2}[/tex]........2

Dividing equation 1 by equation 1

[tex]\frac{R}{R_2}=\frac{\rho l_1}{A_1}\times \frac{0.5A_1}{\rho 2l_1}[/tex]

[tex]R_2=4R[/tex]

Therefore resistance will become 4 times.

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