Resistance of a Wire

Proportionality Relationships for Electrical Conductors

Proportionality Relationships for Electrical Conductors

• The relationship between resistance, length and cross-sectional area can be represented mathematically

  • Resistance is directly proportional to length

  $R \propto L$ 

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

  $R \propto \frac{1}{A}$

Proportional Relationships Between Resistance, Length & Cross-Sectional Area

Resistance is directly proportional to the length of the wire and indirectly proportional to the cross-sectional area

I-V Graphs for Ohmic Resistors, Filament Lamps & Diodes

I-V Graphs for Ohmic Resistors, Filament Lamps & Diodes

• As the potential difference (voltage) across a component is increased, the current in the component also increases

• The precise relationship between voltage and current can be different for different types of components and is shown by an IV graph:

IV Graphs for a Resistor & a Filament Lamp

The IV graph for a resistor is a straight line through the origin, the resistance for a filament lamp changes with temperature

• The IV graph for a resistor is very simple:

  The current is proportional to the potential difference

• This is because the resistor has a constant resistance

   

• For a lamp the relationship is more complicated:

  The current increases at a proportionally slower rate than the potential difference

• This is because:

  • The current causes the filament in the lamp to heat up

  • As the filament gets hot, its resistance increases

  • This opposes the current, causing it to increase at a slower rate 

Effect of Temperature on Resistance

Effect of Temperature on Resistance

• The resistivity of a thermistor behaves in the opposite way to metals

  • This is because it is a type of semiconductor

  • Semiconductors behave in a different way to metals

• The number density of charge carriers (such as electrons) increases with increasing temperature

• Therefore, for a thermistor:

  • An increase in temperature causes a decrease in resistance and resistivity

  • A decrease in temperature causes an increase in resistance and resistivity

• Thermistors are often used in temperature sensing circuits such as thermometers and thermostats

• 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)

Resistance-Temperature Graph for a Thermistor 

Resistance decreases as temperature increases for a thermistor

• 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

Effect of Temperature on a Thermistor

A thermistor has a high resistance at low temperatures and a low resistance at high temperatures