19. Since the mass and density of the material do not change, the volume remains the same. If L

0

is the

original length, L is the new length, A

0

is the original cross-sectional area, and A is the new cross-

sectional area, then L

0

A

0

= LA and A = L

0

A

0

/L = L

0

A

0

/3L

0

= A

0

/3. The new resistance is

R =

ρL

A

=

ρ3L

0

A

0

/3

= 9

ρL

0

A

0

= 9R

0

,

where R

0

is the original resistance. Thus, R = 9(6.0 Ω) = 54 Ω.

Document Outline

• Main Menu
• Chapter 1 Measurement
• Chapter 2 Motion Along a Straight Line
• Chapter 3 Vectors
• Chapter 4 Motion in Two and Three Dimensions
• Chapter 5 Force and Motion I
• Chapter 6 Force and Motion II
• Chapter 7 Kinetic Energy and Work
• Chapter 8 Potential Energy and Conservation of Energy
• Chapter 9 Systems of Particles
• Chapter 10 Collisions
• Chapter 11 Rotation
• Chapter 12 Rolling, Torque, and Angular Momentum
• Chapter 13 Equilibrium and Elasticity
• Chapter 14 Gravitation
• Chapter 15 Fluids
• Chapter 16 Oscillations
• Chapter 17 Waves—I
• Chapter 18 Waves—II
• Chapter 19 Temperature, Heat, and the First Law of Thermodynamics
• Chapter 20 The Kinetic Theory of Gases
• Chapter 21 Entropy and the Second Law of Thermodynamics
• Chapter 22 Electric Charge
• Chapter 23 Electric Fields
• Chapter 24 Gauss’ Law
• Chapter 25 Electric Potential
• Chapter 26 Capacitance
• Chapter 27 Current and Resistance
  • 27.1 - 27.10
    • 27.1
    • 27.2
    • 27.3
    • 27.4
    • 27.5
    • 27.6
    • 27.7
    • 27.8
    • 27.9
    • 27.10
  • 27.11 - 27.20
    • 27.11
    • 27.12
    • 27.13
    • 27.14
    • 27.15
    • 27.16
    • 27.17
    • 27.18
    • 27.19
    • 27.20
  • 27.21 - 27.30
    • 27.21
    • 27.22
    • 27.23
    • 27.24
    • 27.25
    • 27.26
    • 27.27
    • 27.28
    • 27.29
    • 27.30
  • 27.31 - 27.40
    • 27.31
    • 27.32
    • 27.33
    • 27.34
    • 27.35
    • 27.36
    • 27.37
    • 27.38
    • 27.39
    • 27.40
  • 27.41 - 27.50
    • 27.41
    • 27.42
    • 27.43
    • 27.44
    • 27.45
    • 27.46
    • 27.47
    • 27.48
    • 27.49
    • 27.50
  • 27.51 - 27.60
    • 27.51
    • 27.52
    • 27.53
    • 27.54
    • 27.55
    • 27.56
    • 27.57
    • 27.58
    • 27.59
    • 27.60
  • 27.61 - 27.70
    • 27.61
    • 27.62
    • 27.63
    • 27.64
    • 27.65
    • 27.66
    • 27.67
    • 27.68
    • 27.69
    • 27.70
• Chapter 28 Circuits
• Chapter 29 Magnetic Fields
• Chapter 30 Magnetic Fields Due to Currents
• Chapter 31 Induction and Inductance
• Chapter 32 Magnetism of Matter: Maxwell’s Equation
• Chapter 33 Electromagnetic Oscillations and Alternating Current
• Chapter 34 Electromagnetic Waves
• Chapter 35 Images
• Chapter 36 Interference
• Chapter 37 Diffraction
• Chapter 38 Special Theory of Relativity
• Chapter 39 Photons and Matter Waves
• Chapter 40 More About Matter Waves
• Chapter 41 All About Atoms
• Chapter 42 Conduction of Electricity in Solids
• Chapter 43 Nuclear Physics
• Chapter 44 Energy from the Nucleus
• Chapter 45 Quarks, Leptons, and the Big Bang