Wire C and wire D are made from different materials and have length L_C = L_D =

Question

Wire C and wire D are made from different materials and have length L_C = L_D = 4.4 m. The resistivity and diameter of wire C are 2.1 times 10^-6 Ohm middot m and 1.21 mm, and those of wire D are 4.4 times 101^-6 Ohm middot m and 0.73 mm. The wires are joined as shown in the figure and a current of 4.2 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?

Explanation / Answer

(a) rc=d/2 =1.21/2 =0.605 mm

So, A=pir^2 =pi*(0.605*10^-3)^2

=> A=1.15*10^-6 m^2

Rc =pLc/A =(2.1*10^-6)(4.4)/(1.15*10^-6)

Rc = 8.03 ohms

Therefore, Vc =IRc =4.2*8.03 = 33.73 V

(b) rd =d/2 =0.73/2 =0.365mm

A=pi*(0.365*10^-3)^2 = 4.18*10^-7 m^2

Rd =pLd/A =(4.4*10^-6)(4.4)/(4.18*10^-7)

Rd = 46.32 ohm

Vd =IRd =4.2*46.32 = 194.54 V

(c) Pc=Vc*Ic =33.73*4.2 = 141.67 W

(d) Pd=Vd*Id =194.54*4.2 =817.07 W

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