Chapter 26, Problem 051 wire c and wire D are made from different materials and

Question

Chapter 26, Problem 051 wire c and wire D are made from different materials and have length LC = LD = 1.4 m. The resistivity and diameter of wire C are 3.1 × 10-6 -m and 1.32 mm, and those of wire D are 2.5 x 10-6 2.m and o.54 mm. The wires are joined as shown in the figure and a current of 2.6 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? (a) Number (b) Number (c) Number (d) Number Click if you would like to Show Work for this question: Units Units Units Units Open Show Work

Explanation / Answer

Lc = 1.4 m

resistivity of material C = 3.1*10-6 Ohm-m

Diameter of C = 1.32 mm

Area of C=pi*1.322/4=1.368 mm2 = 1.368*10-6 m2

resistance of wire C =(3.1*10-6*1.4)/(1.368*10-6)=3.17 Ohms

Ld = 1.4 m

resistivity of material D = 2.5*10-6 Ohm-m

Diameter of D = 0.54 mm

Area of D=pi*0.542/4=0.229 mm2 = 0.229*10-6 m2

resistance of wire D =(2.5*10-6*1.4)/(0.229*10-6)=15.28Ohms

a) potential difference between 1 and 2 = 2.6*3.17=8.24 volts

b)potential difference between 2 and 3 = 2.6*15.28=39.73 volts

c)rate of energy dissipation between 1 and 2 =i2R= 2.62*3.17=21.43 Watts

d)rate of energy dissipation between 2 ans 3 =i2R= 2.62*15.28=103.29 Watts

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