Resistors (Oxford AQA IGCSE Physics)

Resistors

• The current through a resistor (at a constant temperature) is directly proportional to the potential difference across it

  • This means that the resistance remains constant as the current changes

• A current-potential difference (I-V) graph can be used to represent this relationship:

  • The graph shows a straight line with a constant positive gradient that passes through the origin

  • The gradient is equal to the reciprocal of resistance ()

• This comes from a rearrangement of Ohm's Law:

• Gradient is the change in the y axis over the change in the x axis, so if current is on the y axis and potential difference is on the x axis:

• Flipping the rearranged Ohm's law equation from above (the Δ symbols can be removed for simplicity):

Current-potential difference graph for a fixed resistor

Heating in Resistors

• When an electrical charge flows through a resistor, the resistor gets hot

• This is because of collisions between the moving charges (electrons) and stationary atoms (metal ions) in the wire

  • The ions get in the way of the electrons, resisting their flow

• If the wire is longer, each electron will collide with more ions 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 so more electrons can flow

  • The thicker a wire, the smaller its resistance

Inefficient energy transfer in a filament bulb

• In a filament bulb, almost 100% of energy is transferred from the chemical store of a cell to the thermal store of the filament wires due to resistance

  • This energy is considered wasted, as the function of a bulb is to emit light, not heat

• Only 5% of the energy in the thermal energy store is transferred to the light store due to the glow of the filament

  • A filament bulb is very inefficient

More efficient energy transfer in other lamps

• An efficient system is one where most of the energy going into that system ends up in the form that is wanted

  • For a lightbulb this is to the light energy store and not the thermal energy store

• An inefficient system is one where most of the energy ends up in forms that weren’t wanted

• A compact fluorescent lamp heats up less and therefore wastes less energy than a filament bulb

  • Compact fluorescent lamps are more efficient than filament bulbs

• reduces the electric power consumption for a given luminosity by 80% compared to a filament lamp

  • Hence, a more efficient lightbulb is cheaper to run

• Assuming a constant usage (24 hours a day) and a tariff of 10p, or £0.10 per kWh the annual cost of running each lightbulb is:

  • An LED is £10.51

  • A CFL is £13.14

  • A halogen is £36.79

  • An incandescent is £52.56

• Therefore, an LED lightbulb is about 5 times cheaper to run than a filament bulb

Efficiency of appliances

• When purchasing new appliances it is possible to choose how efficiently they transfer energy for their intended purpose

• More efficient appliances normally bear a higher purchase cost but cost less to run

• On most appliances, manufacturers provide energy rating labels to allow customers to make comparisons

• Energy rating labels describe:

  • The energy consumption of the appliance in kWh per year

  • The efficiency of the appliance by assigning a band value from A to G, where A is the most efficient and G is the least efficient

Energy efficiency rating label for a fridge