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# Values of x and y

ACTSCI-R16MOG

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

The resistance of a wire is given by the formula: $R = β l^xr^y$, where $“l”$ is the length of the wire, $“r”$ is the radius of the cross section and $“β”$ is a constant.

Find the values of $x$ and $y$ from the information given in the passage.

A

$x = 1; y = 1$

B

$x = 1; y = 2$

C

$x = 1; y = -1$

D

$x = 1; y = -2$