Question
Asked Aug 1, 2019

Wire C and wire D are made from different materials and have length LC = LD = 3.1 m. The resistivity and diameter of wire C are 3.3 × 10-6 Ω·m and 1.03 mm, and those of wire D are 1.2 × 10-6 Ω·m and 0.72 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?

C
-Lp
Lc
3
1
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C -Lp Lc 3 1

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Step 1

The electric potential difference between point 1 and 2 is the potential drop in wire C.

Write the expression for resistance of a circular wire C

Here, RC is the resistance of the wire C, ρC is its resistivity, LC is its length and dC is its diameter.

Substitute 3.3×10-6 Ω·m for ρC, 3.1 m for LC and 1.03 mm for dC

Rc
T(de/2)
(3.3x10 m(3.1 m)
T(1.03 mm/2)10-3 m
1 mm
12.27 Q
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Rc T(de/2) (3.3x10 m(3.1 m) T(1.03 mm/2)10-3 m 1 mm 12.27 Q

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Step 2

Write the expression for potential drop in wire C

Here, VC is the potential drop in wire C and iC is the current flowing through it.

Ve icRc
(I)
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Ve icRc (I)

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Step 3

Substitute 12.27 Ω for RC and 2.6 A for iC in equation (I) to find VC

Thus, the electric poten...

V (2.6 A) (12.27 n
=31.92 V
32 V
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V (2.6 A) (12.27 n =31.92 V 32 V

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