(1) Wire C and wire D are made from different materials and have length L C = L

Question

(1)

Wire C and wire D are made from different materials and have length LC = LD = 1.8 m. The resistivity and diameter of wire C are 3.4 × 10-6 ?·m and 1.14 mm, and those of wire D are 2.5 × 10-6 ?·m and 0.66 mm. The wires are joined as shown in the figure and a current of 4.0 A is set up in them. What is the electric potential difference between (a) points 1 and 2 and (b) points 2 and 3? What is the rate at which energy is dissipated between (c) points 1 and 2 and (d)points 2 and 3?

(2)

If the gauge number of a wire is increased by 6, the diameter is halved; if a gauge number is increased by 1, the diameter decreases by the factor 21/6. Knowing this, and knowing that 800 ft of 10-gauge wire has a resistance of approximately 1.44 ?, calculate the resistance of 19 ft of 23-gauge wire made of the same material.

Thanks.

Explanation / Answer

1)

Rc = c*Lc/ [(/4)dc^2]

Pc = i^2Rc

In this problem figure is not visible hopefully this formulae helpfull for you.

2)

The gauge increases by
23-10 = 13 gauge numbers.

The diameter decreases by a factor of
2^(13/6) = 2^2.16 = 4.47

So the area decreases by a factor of
4.47^2 = 20

Resistance is inversely proportional to area, so the resistance increases by a factor of 20.

23 gauge will have a resistance of:
1.44ohm/800ft x 20 = 28.8ohm/800ft

19 feet of 23 gauge will have a resistance of:
28.8ohm/800ft x 19ft = 0.684 ohms

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