O Level Physics 5054 Paper 41, Oct/Nov 2025

The student is provided with the circuit shown in Fig. 1.1. The coil of wire is the small electric heater. Fig. 1.1 Draw on the circuit in Fig. 1.1 to show a voltmeter connected to measure the potential difference across the heater.

The student is also provided with: • a thermometer • a stirrer • a measuring cylinder containing water at room temperature • a stopwatch. Fig. 1.2 shows the volume of water $W$ in the measuring cylinder. Fig. 1.2 Record the volume of water $W$. $$W=\text{.................................................. }\mathrm{c}{\mathrm{m}}^3$$

The student: • pours the water from the measuring cylinder into the beaker containing the heater • makes sure that the heater is covered by water • closes the switch • records the readings on the voltmeter and ammeter • opens the switch. Fig. 1.3 shows the reading on the voltmeter and on the ammeter when the switch is closed. Fig. 1.3 Record the potential difference $V$ and the current $I$. $$V=\text{........................................................... }\mathrm{V}$$ $$I=\text{............................................................ }\mathrm{A}$$

The thermometer is placed in the water in the beaker. Fig. 1.4 shows the initial temperature ${\theta }_0$ of the water. Fig. 1.4 Record the initial temperature ${\theta }_0$ of the water in the beaker. $${\theta }_0={\text{..................................................... }}^{\circ }\mathrm{C}$$

The student: • closes the switch and immediately starts the stopwatch • leaves the heater switched on for 5 minutes • stirs the water while the heater is switched on • opens the switch • continues to stir the water for a further minute • records the final temperature ${\theta }_F$. The final temperature ${\theta }_F$ is $24.5{}^{\circ }\mathrm{C}$. Calculate the temperature change $\mathrm{\Delta }\theta$. Use the equation shown. $$\mathrm{\Delta }\theta ={\theta }_F-{\theta }_0$$ $$\mathrm{\Delta }\theta ={\text{.................................................... }}^{\circ }\mathrm{C}$$

Explain why the student continues to stir the water for a further minute after the heater is switched off.

The energy $Q_H$ supplied by the heater is given by $$Q_H=I\times V\times t$$ where $t=300\mathrm{s}$. Calculate $Q_H$. Show your working. $$Q_H=\text{...................................................... }\mathrm{J}$$

The energy $Q_W$ gained by the water is given by the equation shown. $$Q_W=W\times 4.2\times \mathrm{\Delta }\theta$$ Calculate $Q_W$ using your value of $W$ from (b)(i) and your value of $\mathrm{\Delta }\theta$ from (c)(ii). Show your working. $$Q_W=\text{...................................................... }\mathrm{J}$$

The efficiency of the heater is given by the equation shown. $$\text{efficiency}=\frac{Q_W}{Q_H}$$ Calculate the efficiency of the heater. Show your working. $$\text{efficiency}=\text{.........................................................}$$

Suggest one change that can be made to the apparatus used in this investigation that will increase the efficiency of the heater.

Fig. 2.1 shows a top view of the transparent block. Fig. 2.1 On Fig. 2.1, draw a normal to the line XY at point M and extend it above and below the line XY.

Draw a line from M at an angle of ${40}^{\circ }$ to the normal to the left of the normal above line XY so that the angle between the drawn line and the normal is ${40}^{\circ }$. The ${40}^{\circ }$ angle is the angle of incidence. Label the top left-hand end of the line as point L.

The student uses an illuminated slit to shine a narrow ray of light along the line LM. The student marks the emerging ray with two crosses as shown in Fig. 2.1. Join the marked crosses and extend the line to meet the lower end of the outline of the block. Label this as point P.

Join the points M and P with a straight line.

The angle of refraction $r$ is the angle between the line MP and the normal drawn in (a)(i). Measure and record angle $r$. $$r={\text{....................................................... }}^{\circ }$$

The refractive index $n$ of the transparent block is given by the equation shown. $$n=\frac{\sin {40}^{\circ }}{\sin r}$$ Calculate $n$ and give your answer to 2 significant figures. $$n=\text{.......................................................}$$

Suggest how you could change the experiment to make sure that your value of $n$ is accurate.

Theory states that the angle between the emerging ray and the normal at the point that the ray emerges should be the same as the angle of incidence. In (a)(i), the angle of incidence is given as ${40}^{\circ }$. Add another normal to your diagram. Measure and record the angle $\alpha$ between the emerging ray and the normal. $$\alpha ={\text{............................................................. }}^{\circ }$$ Explain whether your measurements agree with this theory.

The student: • places a small empty dish on a top pan balance. Fig. 3.1 shows the reading on the balance. Fig. 3.1 • adds 5 marbles to the dish. Fig. 3.2 shows the new reading on the balance. Fig. 3.2 Use the readings from Fig. 3.1 and Fig. 3.2 to calculate the mass of the 5 marbles. Show your working. $$\text{mass of 5 marbles}=\text{...................................................... }\mathrm{g}$$

Calculate the average mass of 1 marble. $$\text{average mass of 1 marble}=\text{...................................................... }\mathrm{g}$$

The student uses the apparatus shown in Fig. 3.3. Fig. 3.3 The distance between the bench and the bottom side of the rule at the $90\mathrm{c}\mathrm{m}$ mark is $h$. The ramp is initially arranged with height $h=4.0\mathrm{c}\mathrm{m}$ above the bench. procedure The student: • places a marble on the gap between the rules so that its right-hand edge is on the $90.0\mathrm{c}\mathrm{m}$ mark • releases the marble and records the time $t_1$ for the marble to roll down the ramp until it hits the stopper • repeats the experiment two more times. The second and third measurements of time are recorded as $t_2$ and $t_3$. Times $t_1$, $t_2$ and $t_3$ are shown. $$t_1=2.16\mathrm{s}{t}_2=2.23\mathrm{s}{t}_3=2.25\mathrm{s}$$ Calculate the average time $t_{\mathrm{a}\mathrm{v}}$ for the marble to travel $90.0\mathrm{c}\mathrm{m}$ down the ramp. $$t_{\mathrm{a}\mathrm{v}}=\text{...................................................... }\mathrm{s}$$

The procedure in (b)(i) is repeated for heights $h=6.0\mathrm{c}\mathrm{m}$, $8.0\mathrm{c}\mathrm{m}$, $10.0\mathrm{c}\mathrm{m}$ and $12.0\mathrm{c}\mathrm{m}$. All results are recorded in Table 3.1. Complete Table 3.1, finding the average time $t_{\mathrm{a}\mathrm{v}}$ for each value of $h$. Include the results from (b)(i) in the table. Give all values to a suitable number of decimal places. Table 3.1

On the grid provided in Fig. 3.4 on page 13, plot a graph of $t_{\mathrm{a}\mathrm{v}}\mathrm{/}\mathrm{s}$ on the y-axis against $h\mathrm{/}\mathrm{c}\mathrm{m}$ on the x-axis. Draw a line of best fit through your points. You do not need to start your axes at (0, 0).

Describe the relationship between $h$ and $t_{\mathrm{a}\mathrm{v}}$.

Use your graph to find $t_{\mathrm{a}\mathrm{v}}$ when $h=7.0\mathrm{c}\mathrm{m}$. Show on the graph how you find $t_{\mathrm{a}\mathrm{v}}$ for $h=7.0\mathrm{c}\mathrm{m}$. $$t_{\mathrm{a}\mathrm{v}}=\text{...................................................... }\mathrm{s}$$

The average speed $v$ of the marble is given by: $$v=\frac{0.90}{t_{\mathrm{a}\mathrm{v}}}$$ Find the average speed $v$ of the marble when $h=7.0\mathrm{c}\mathrm{m}$. Give the unit of your answer. $$\text{average speed }v=\text{................................... unit ..............}$$