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Moderate

Plot of Resistance and Radius

ACTSCI-JRNTJI

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

Which of these is the correct plot of the change in resistance of a wire with change in the radius of its cross section?

(Length of the wire and the temperature are constant).

A
B
C
D