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Unformatted text preview: n leads to r1 = 1.55 mm.
(b) The 4r22 = 1.5r32 relation leads to r2 = 1.22 mm.
25. Since the mass density of the material does not change, the volume remains the same.
If L0 is the original length, L is the new length, A0 is the original crosssectional area, and
A is the new crosssectional area, then L0A0 = LA and A = L0A0/L = L0A0/3L0 = A0/3. The
new resistance is
ρL ρ 3 L0
ρL
=
= 9 0 = 9 R0 ,
R=
A
A0 / 3
A0
where R0 is the original resistance. Thus, R = 9(6.0 Ω) = 54 Ω.
26. The absolute values of the slopes (for the straightline segments shown in the graph of
Fig. 2625(b)) are equal to the respective electric field magnitudes. Thus, applying Eq.
265 and Eq. 2613 to the three sections of the resistive strip, we have
i
J1 = A = σ1 E1 = σ1 (0.50 × 103 V/m)
i
J2 = A = σ2 E2 = σ2 (4.0 × 103 V/m)
i
J3 = A = σ3 E3 = σ3 (1.0 × 103 V/m) .
We note that the current densities are the same since the values of i and A are the same
(see the problem statement) in the three sections, so J1 = J2 = J3 .
(a) Thus we see that σ1 = 2σ3 = 2 (3.00 × 107(Ω · m)−1 ) = 6.00 × 107 (Ω · m)−1. 1046 CHAPTER 26 (b) Similarly, σ2 = σ3/4 = (3.00 × 107(Ω · m)−1 )/4 = 7.50 × 106 (Ω · m)−1 .
27. The resistance of conductor A is given by
RA = ρL
2
prA , where rA is the radius of the conductor. If ro is the outside diameter of conductor B and ri
is its inside diameter, then its crosssectional area is π(ro2 – ri2), and its resistance is
RB =
The ratio is b ρL π ( ro2 − ri 2 ) gb . 2 g 1.0 mm − 0.50 mm
R A ro2 − ri 2
=
=
2
2
RB
rA
0.50 mm b g 2 = 3.0. 28. The crosssectional area is A = πr2 = π(0.002 m)2. The resistivity from Table 261 is
ρ = 1.69 × 10−8 Ω · m. Thus, with L = 3 m, Ohm’s Law leads to V = iR = iρL/A, or
12 × 10−6 V = i (1.69 × 10−8 Ω · m)(3.0 m)/ π(0.002 m)2
which yields i = 0.00297 A or roughly 3.0 mA.
29. First we find the resistance of the copper wire to be
R= ρL
A (1.69 ×10
= −8 Ω ⋅ m ) ( 0.020 m ) π (2.0 ×10 m)
−3 2 = 2.69 × 10−5 Ω . With potential difference V = 3.00 nV ,...
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This document was uploaded on 02/26/2014 for the course PHYS 2b at UCSD.
 Fall '08
 schuller
 Magnetism, Work

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