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Stretched Wire

ACTSCI-KXAWJJ

The electrical resistance $“R”$ of a metal is given by the formula:

$$ R = p (l/A) $$

The table below shows the electrical resistance of a wire (made of metal “Z”) of length “l” and cross-sectional area “A”, at different temperatures.

Table 3.1

Temperature Resistance (in ohm)
20$^\circ$ C 40
25$^\circ$ C 41
30$^\circ$ C 42
35$^\circ$ C 43

The table below shows the resistances of wires of different lengths made out of the same metal (Z) at 20° C. The cross-sectional area of these wires is equal.

Table 3.2

Length (in meter) Resistance (in ohm)
1 40
1.05 42
1.1 44
1.15 46

The table below shows the resistances of wires of different cross-sectional areas made of the same metal (Z) at 20° C. The length of these wires is equal.

Table 3.3

Cross sectional area (in 10-8 m$^2$) Resistance (in ohm)
1 40
2 20
3 13.33
4 10

At $20° C$, a 1-meter long wire made of the metal $“Z”$ with cross-sectional area $1 x 10^{-8} m^2$ is stretched to make it $4$ meters long.

What will be its new resistance?

A

$160 \ ohm$

B

$40 \ ohm$

C

$640 \ ohm$

D

$2.5 \ ohm$