Resistance of a Wire (Cambridge O Level Physics)

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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 space proportional to space L 

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

R space proportional to space 1 over A

    

Proportional Relationships Between Resistance, Length & Cross-Sectional Area

Factors affecting resistance, IGCSE & GCSE Physics revision notes

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

  • 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

IV graphs, IGCSE & GCSE Physics revision notes

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

  • 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 

Thermistor graph, downloadable AS & A Level Physics revision notes

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

Thermistor diagram, downloadable AS & A Level Physics revision notes

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

Worked example

A thermistor is connected in series with a resistor R and a battery.

WE - thermistor in circuit question image, downloadable AS & A Level Physics revision notes

The resistance of the thermistor is equal to the resistance of R at room temperature.

Which statement describes the effect when the temperature of the thermistor decreases?

A.     The p.d across the thermistor increases

B.     The current in R increases

C.     The current through the thermistor decreases

D.     The p.d across R increases

Answer: A

Step 1: Outline the nature of a thermistor

  • The resistance of the thermistor increases as the temperature decreases

Step 2: Consider the properties of current in a series circuit

  • Since the thermistor and resistor R are connected in series, the current I in both of them is the same

Step 3: Consider a relevant equation

  • Ohm’s law states that V = IR
  • Since the resistance of the thermistor increases, and I is the same, the potential difference V across it increases

Step 4: State the conclusion

  • Therefore, statement A is correct

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Leander

Author: Leander

Expertise: Physics

Leander graduated with First-class honours in Science and Education from Sheffield Hallam University. She won the prestigious Lord Robert Winston Solomon Lipson Prize in recognition of her dedication to science and teaching excellence. After teaching and tutoring both science and maths students, Leander now brings this passion for helping young people reach their potential to her work at SME.