1. 1
   A hairdryer has a heating element with a resistance of 20 $\Omega$. When switched on, a current of 11.5 A passes through the heating element for 3 minutes. The hairdryer is connected to the UK mains supply.

   (a)

   A hairdryer heating element has a resistance of 20 $\Omega$ and a current of 11.5 A passes through it when it is switched on. Which equation should be used to calculate the power transferred by the heating element using only these two values?

   [1 mark]

   • AP = I $\times$ V
   • BP = I^2 $\times$ R
   • CP = $\dfrac{E}{t}$
   • DE = Q $\times$ V

   (b)

   The hairdryer is used for 3 minutes. Which quantity, if given directly, would allow the total energy transferred by the heating element to be calculated using E = I × V × t without first calculating anything else?

   [1 mark]

   • AThe resistance of the heating element only
   • BThe charge that passes through the heating element
   • CThe potential difference across the heating element
   • DThe mass of the heating element

   (c)

   Calculate the potential difference across the heating element while the current of 11.5 A passes through it, and calculate the power transferred by the heating element. Use V = I × R and P = I × V. Give your answers with units.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A toaster has a heating element connected to the 230 V UK mains supply. When switched on, a current of 4 A passes through the heating element for 90 seconds to toast one cycle of bread. The toaster casing does not heat up noticeably during use.

   (a)

   A student wants to find how much energy is transferred by the toaster's heating element in one full toasting cycle, using E = I × V × t. Which additional piece of information, beyond the current and potential difference already known, is essential?

   [1 mark]

   • AThe colour of the toaster casing
   • BThe number of slices being toasted
   • CThe mass of bread being toasted
   • DThe time for which the toaster operates

   (b)

   The toaster casing stays cool while the heating element becomes very hot. Which statement best explains why the heating element heats up so much more than the casing?

   [1 mark]

   • AThe current passes through the heating element, and its resistance causes electrical energy to be dissipated as heat there due to electron-ion collisions
   • BThe casing is made of a magnetic material, so it repels heat
   • CThe casing has a higher specific heat capacity, so it cannot be heated at all
   • DThe heating element has a lower potential difference across it than the casing

   (c)

   Calculate the total energy transferred by the heating element during the 90 second toasting cycle, using E = I × V × t. Give your answer with units.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A student compares two electric kettles, X and Y, used in a school science lab. Kettle X has a heating element made from a wire with a higher resistance than the heating element in Kettle Y. Both kettles are connected to the same 230 V mains supply, are filled with the same volume of water at the same starting temperature, and are switched on for the same length of time.

   (a)

   A student compares two electric kettles. Kettle X has a heating element made from a wire with a higher resistance than Kettle Y. Both kettles are connected to the same 230 V mains supply and are used to heat the same volume of water. Explain, in terms of power, why Kettle X and Kettle Y transfer electrical energy to the water at different rates. Use the equation P = V²/R, derived from P = I × V and V = I × R, to support your answer.

   [3 marks]

   (b)

   Kettle Y draws a current of 10 A from the 230 V supply. Calculate the power rating of Kettle Y using P = I × V, then calculate the energy transferred by Kettle Y if it is switched on for 4 minutes, using E = P × t. Give both answers with units.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   An electrician is wiring a new kitchen extension. Several high-power appliances, including an oven and a combination microwave, will be connected to the consumer unit via cables running under the floor. The electrician must choose the thickness of the copper cable for this circuit. She knows that a thinner cable of the same material has a higher electrical resistance per metre than a thicker cable, and that the cables will be hidden under the floor once installed, making later repairs difficult and costly.

   (a)

   An electrician is choosing cables to wire a new kitchen extension carrying current to several high-power appliances from the consumer unit. She must choose between cables made from wires of different thicknesses (cross-sectional areas), knowing that a thinner wire has a higher resistance per metre than a thicker wire of the same material. Explain, using ideas about electron-ion collisions and energy dissipation, why using a wire with too high a resistance for the cable run could be unsafe and wasteful, and describe how the electrician could reduce unwanted energy transfer in the cables while keeping costs reasonable.

   [6 marks]

   (b)

   The extension's oven has a power rating of 3000 W and is designed to run from the 230 V mains supply for an average of 45 minutes per use. Explain how the electrician could estimate the current the cable must safely carry, and describe, with reference to power ratings and stored energy, how a domestic user could reduce the total energy used by the oven over a week without changing the appliance itself.

   [6 marks]

   Total for question 4: 12 marks

End of questions