Question 23M.2.HL.TZ2.4
| Date | May 2023 | Marks available | [Maximum mark: 12] | Reference code | 23M.2.HL.TZ2.4 |
| Level | HL | Paper | 2 | Time zone | TZ2 |
| Command term | Calculate, Explain, Outline, Show that, State | Question number | 4 | Adapted from | N/A |
An electrically heated pad is designed to keep a pet warm.
The pad is heated using a resistor that is placed inside the pad. The dimensions of the resistor are shown on the diagram. The resistor has a resistance of 4.2 Ω and a total length of 1.25 m.
diagram not to scale
When there is a current in the resistor, the temperature in the pad changes from a room temperature of 20 °C to its operating temperature at 35 °C.
The designers state that the energy transferred by the resistor every second is 15 J.
Calculate the current in the resistor.
[1]
I = « =» 1.9 «A» ✓
The designers wish to make the resistor from carbon fibre.
The graph shows the variation with temperature, in Kelvin, of the resistivity of carbon fibre.
The resistor has a cross-sectional area of 9.6 × 10−6 m2.
Show that a resistor made from carbon fibre will be suitable for the pad.
[3]
ALTERNATIVE 1 (Calculation of length)
Read off from graph [2.8 − 3.2 × 10−5 Ω m]✓
Use of ✓
l = 1.3 − 1.4 «m» ✓
ALTERNATIVE 2 (Calculation of area)
Read off from graph [2.8 − 3.2 × 10−5 Ω m]✓
Use of ✓
A = 8.3 − 9.5 × 10−6 «m2» ✓
ALTERNATIVE 3 (Calculation of resistance)
Read off from graph [2.8 − 3.2 × 10−5 Ω m]✓
Use of ✓
R = 3.6 − 4.2 «Ω» ✓
ALTERNATIVE 4 (Calculation of resistivity)
Use of ✓
= 3.2 × 10−5 «Ω m» ✓
Read off from graph 260 – 280 K ✓
The power supply to the pad has a negligible internal resistance.
State and explain the variation in current in the resistor as the temperature of the pad increases.
[2]
«Resistivity and hence» resistance will decrease ✓
«Pd across pad will not change because internal resistance is negligible»
Current will increase ✓
When there is a current in the resistor, magnetic forces act between the resistor strips.
For the part of the resistor labelled RS,
outline the magnetic force acting on it due to the current in PQ.
[1]
«The force is» away from PQ/repulsive/to the right ✓
state and explain the net magnetic force acting on it due to the currents in PQ and TU.
[2]
The magnetic fields «due to currents in PQ and TU» are in opposite directions
OR
There are two «repulsive» forces in opposite directions ✓
Net force is zero ✓
The design of the pad encloses the resistor in a material that traps air. The design also places the resistor close to the top surface of the pad.
Explain, with reference to thermal energy transfer, why the pad is designed in this way.
[3]
Air is a poor «thermal» conductor ✓
Lack of convection due to air not being able to move in material ✓
Appropriate statement about energy transfer between the pet, the resistor and surroundings ✓
The rate of thermal energy transfer to the top surface is greater than the bottom «due to thinner material» ✓
Accept air is a good insulator