Resistance and Resistivity

• • Resistance is defined as the opposition to current
  • For a given potential difference: The higher the resistance the lower the current
• • Resistance is measured in Ohms (Ω)
  • Ω is the Greek capital letter 'Omega'
  • An Ohm is defined as one volt per ampere (1 V A-1)
• • The resistance controls the size of the current in a circuit
  • A higher resistance means a smaller current
  • A lower resistance means a larger current
• • Ohm’s law states:

  For a conductor at a constant temperature, the current through it is proportional to the potential difference across it

  • Constant temperature implies constant resistance
• Measuring the variation of current with potential difference through a fixed resistor will produce a straight line graph, 
• • Since the gradient is constant, the resistance R of the resistor can be calculated by using 1 ÷ gradient of the graph
  • An electrical component obeys Ohm’s law if its graph of current against potential difference is a straight line through the origin
  • A resistor does obey Ohm’s law
  • A filament lamp does not obey Ohm’s law
• • For a non-ohmic conductor, such as
  • A semiconductor diode, the I–V graph is a horizontal line that goes sharply upwards
  • An LED (light-emitting diode), the I–V graph is similar to the semiconductor diode, since it is a specific diode that emits visible light
  • A filament lamp, the I–V graph has an 'S' shaped curve
  • A thermistor, the I–V graph is a curved line with increasing gradient through the origin
• Ohmic Conductor

  • The I–V graph for an ohmic conductor at constant temperature e.g. a resistor is very simple:
  • The current is directly proportional to the potential difference
  • This is demonstrated by the straight-line graph through the origin
• Semiconductor Diode . A diode is used in a circuit to allow current to flow only in a specific direction

  • When the current is in the direction of the arrowhead symbol, this is forward bias
  • This is shown by the sharp increase in potential difference and current on the right side of the graph
  • When the diode is switched around, it does not conduct and is called reverse bias
  • This is shown by a zero reading of current or potential difference on the left side of the graph which then goes steeply vertically down
• Filament Lamp

  • The I–V graph for a filament lamp shows the current increasing at a proportionally slower rate than the potential difference
  • This is because:
  • As the current increases, the temperature of the filament in the lamp increases
  • Since the filament is a metal, the higher temperature causes an increase in resistance
  • Resistance opposes the current, causing the current to increase at a slower rate
  • Where the graph is a straight line, the resistance is constant
  • The resistance increases as the graph curves
  • The filament lamp obeys Ohm's Law for small voltages
• Thermistor

  • The I–V graph for a thermistor is a shallow curve upwards
  • The increase in the potential difference results in an increase in current which causes the temperature of the thermistor to rise
  • As its temperature rises, its resistance decreases
  • This means even more current is able to flow through
  • Since the current is not directly proportional to the potential difference (the graph is still curved), the thermistor does not obey Ohm's Law
• • A light-dependent resistor (LDR) is a non-ohmic conductor and sensory resistor
  • Its resistance automatically changes depending on the light energy falling onto it (illumination)
  • As the light intensity increases, the resistance of an LDR decreases
• • LDRs can be used as light sensors, so, they are useful in circuits which automatically switch on lights when it gets dark, for example, street lighting and garden lights
  • In the dark, its resistance is very large (millions of ohms)
  • In bright light, its resistance is small (tens of ohms)
• • All materials have some resistance to the flow of charge
  • As free electrons move through a metal wire, they collide with ions which get in their way
  • As a result, they transfer some, or all, of their kinetic energy on collision, which causes electrical heating
• • Since current is the flow of charge, the ions resisting their flow causes resistance
  • Resistance depends on the length of the wire, the cross-sectional area through which the current is passing and the resistivity of the material
• he resistivity equation shows that:

  • The longer the wire, the greater its resistance
  • The thicker the wire, the smaller its resistance
• • Resistivity is a property that describes the extent to which a material opposes the flow of electric current through it
  • It is a property of the material, and is dependent on temperature
  • Resistivity is measured in Ω m
• Metals

  • All solids are made up of vibrating atoms
  • As the temperature rises, the ions vibrate with a greater frequency and amplitude
  • The electrons collide with the vibrating atoms which impede their flow, hence the current decreases
  • So, if the current decreases, then the resistance will increase (from V = IR)
  • Therefore, its resistivity will increase since ρ ∝ R (if the area A and length L is constant)
  • For a metallic conductor which obeys Ohm's law:
  • An increase in temperature causes an increase in resistance and resistivity
  • A decrease in temperature causes a decrease in resistance and resistivity
• Semiconductors

  • The resistivity of semiconductors behaves in the opposite way to metals
  • The number density of charge carriers (such as electrons) increases with increasing temperature
  • Therefore, for a semiconductor:
  • An increase in temperature causes a decrease in resistance and resistivity
  • A decrease in temperature causes an increase in resistance and resistivity
  • One example of this is a thermistor
  • This is often used in temperature sensing circuits such as thermometers and thermostats
  • This is only for semiconductors with a negative temperature coefficient (NTC)
• • A thermistor is a non-ohmic conductor and sensory resistor whose resistance varies with temperature
  • Most thermistors are negative temperature coefficient (ntc) components
  • This means that if the temperature increases, the resistance of the thermistor decreases (and vice versa)
• • Thermistors are temperature sensors and are used in circuits in ovens, fire alarms and digital thermometers
  • As the thermistor gets hotter, its resistance decreases
  • As the thermistor gets cooler, its resistance increases