Resistance of a Wire (CIE IGCSE Physics: Co-ordinated Sciences (Double Award))

Extended tier only

• As electrons pass through a wire, they collide with the metal ions in the wire
• These collisions transfer energy away from the kinetic store of the electrons, which causes them to slow down
• The energy from the electrons is transferred to the kinetic store of the vibrating metal ions
  • This causes the vibration of the ions to increase (increased temperature)
  • As the vibration of the ions increases, the more the electrons collide with them (increased resistance)

Electron collisions in a metal wire

Electrons collide with metal ions, which resist their flow

• If the wire is longer, each electron will collide with more ions, and so there will be more resistance:
  • The longer a wire, the greater its resistance

• If the wire is thicker (greater diameter) there is more space for the electrons and so more electrons can flow:
  • The thicker a wire, the smaller its resistance

The relationship between resistance, length and cross-sectional area

• The relationship between resistance, length and cross-sectional area can be represented mathematically
• Resistance is directly proportional to length

• This means that
  • doubling the length will double the resistance
  • halving the length will halve the resistance

• Resistance is inversely proportional to cross-sectional area (width, or thickness) 

• This means that
  • doubling the cross-sectional area will halve the resistance
  • halving the cross-sectional area will double the resistance

Effect of length and cross-sectional area on resistance

The mathematical relationship between length and width of the wire and the resistance