Physics 5054/41 — May/June 2025

Walkthrough

To read the ammeter in Fig. 1.2:

1. The scale is labelled from $0$ to $1.0\text{ A}$ with major numbered divisions every $0.2\text{ A}$.
2. Between $0.2\text{ A}$ and $0.4\text{ A}$, there are 10 small divisions, meaning each small division represents $\frac{0.2}{10} = 0.02\text{ A}$.
3. The pointer is exactly halfway between $0.2$ and $0.4$, on the 5th tick mark: $0.2 + (5 \times 0.02) = 0.30\text{ A}$.

To read the voltmeter in Fig. 1.2:

1. The scale is numbered $0$ to $5\text{ V}$ with major numbered marks every $1\text{ V}$.
2. Between $2\text{ V}$ and $3\text{ V}$, there are 10 small divisions, so each small division represents $\frac{1}{10} = 0.1\text{ V}$.
3. The pointer is on the 8th small mark past $2\text{ V}$ (or 2 marks before $3\text{ V}$), which gives $2.0 + (8 \times 0.1) = 2.8\text{ V}$.

Key Takeaways

• Always determine the value of one small division on an analogue scale before taking a reading.
• Include appropriate precision based on the scale divisions.

Common Mistakes

• Reading the ammeter pointer incorrectly (e.g. miscounting divisions as $0.01$ or $0.05$).
• Forgetting the trailing zero on $0.30\text{ A}$ when the precision allows it (though $0.3$ is also credited).

Things to Be Careful About

• Ensure correct matching of the reading to the corresponding symbol ($I_L$ for current in amperes, $V_L$ for voltage in volts).

Walkthrough

When current flows through a circuit, electrical energy is converted into thermal energy due to resistance. Opening the switch between measurements ensures that:

1. The lamp and connecting wires do not heat up, which would otherwise change their resistance and introduce temperature-dependent errors.
2. If batteries/cells are used, it prevents them from discharging unnecessarily.

Key Takeaways

• Keeping switches closed for prolonged periods in circuit experiments causes heating effects that alter resistance.

Common Mistakes

• Giving vague answers like "for safety" without specifying overheating or power drainage.

Things to Be Careful About

• Mentioning specific effects: heating of components/wires or running down the power source.

Walkthrough

1. Use Ohm's law / resistance formula $R = \frac{V}{I}$.
2. Substitute the values from part (a)(i): $V = 2.8\text{ V}$ and $I = 0.30\text{ A}$.
3. Calculate the unrounded value:

1. The question explicitly asks for 2 significant figures, so $9.333\ldots$ rounds to $9.3\ \Omega$.

Key Takeaways

• Always read the significant figure requirement in calculation questions.
• $R = \frac{V}{I}$ gives the resistance in ohms ($\Omega$) when $V$ is in volts and $I$ is in amperes.

Common Mistakes

• Leaving the answer as $9.33\ \Omega$ or $\frac{28}{3}\ \Omega$, ignoring the "2 significant figures" instruction.

Things to Be Careful About

• Rounding properly: 3 is followed by 3, so round down to $9.3$.

Walkthrough

To draw the modified circuit:

1. Maintain the series loop containing the power supply, open/closed switch, and ammeter.
2. In the branch between $\text{P}$ and $\text{Q}$, place the fixed resistor (represented by a standard rectangle symbol) in series with the lamp (a circle with an 'X' inside).
3. Connect the voltmeter in parallel across both the resistor and the lamp together, so that it measures the combined potential difference.

Key Takeaways

• A voltmeter is always connected in parallel across the specific component or combination of components being measured.
• Series components are connected one after another in a single loop.

Common Mistakes

• Drawing the voltmeter across only the lamp or only the resistor.
• Drawing the resistor in parallel with the lamp.
• Using incorrect component symbols (e.g. a zigzag line or missing circle for the lamp).

Things to Be Careful About

• Standard circuit symbols: rectangle for a fixed resistor, circle with cross for a filament lamp, circle with 'A' for ammeter, circle with 'V' for voltmeter.

Walkthrough

1. Read $I_C$ from Fig. 1.3:
   • Major divisions are every $0.2\text{ A}$ with 10 small tick subdivisions, so each small tick is $0.02\text{ A}$.
   • The pointer is 1 small division before $0.2\text{ A}$, which is $0.20 - 0.02 = 0.18\text{ A}$.
2. Calculate $R_C$:
   • The question states the voltmeter reading does not change, so $V = 2.8\text{ V}$.
   • Substitute $V$ and $I_C$ into $R = \frac{V}{I}$:

• Quoting to 2 or 3 significant figures gives $15.6\ \Omega$ (or $16\ \Omega$).

Key Takeaways

• Reading before a major mark involves subtracting divisions ($0.20 - 0.02 = 0.18\text{ A}$).
• Use the stated condition ($V$ is unchanged) to obtain the potential difference needed for calculation.

Common Mistakes

• Misreading the scale as $0.16\text{ A}$ (counting 2 marks backwards instead of 1).

Things to Be Careful About

• Ensure you carry forward your $V$ value from part (a)(i).

Walkthrough

1. Use the provided formula:

1. Substitute the value of $R_C$ calculated in (b)(ii), which is $15.6\ \Omega$:

(If an unrounded value of $15.56$ was used, $R_L = 5.56\ \Omega$ or $5.6\ \Omega$ is obtained).

Key Takeaways

• In a series circuit, the total resistance is the sum of the individual resistances ($R_{\text{total}} = R_1 + R_2$), hence $R_{\text{lamp}} = R_{\text{total}} - R_{\text{resistor}}$.

Common Mistakes

• Forgetting to carry forward the calculated value of $R_C$ from part (b)(ii).

Things to Be Careful About

• Error carried forward (ecf) applies from part (b)(ii).

Walkthrough

1. Change in brightness: Adding the $10\ \Omega$ resistor in series increases the total resistance of the circuit. Since the potential difference across the combination remains the same, the current decreases from $0.30\text{ A}$ to $0.18\text{ A}$. Less current and less power dissipated in the lamp means the lamp is dimmer.
2. Explanation: Either of two physical explanations is accepted:
   • Circuit view: The circuit resistance is greater, which reduces the current through the lamp, reducing its brightness.
   • Filament temperature view: Because the current is smaller, less thermal energy is dissipated, the filament operates at a lower temperature, and its resistance decreases (from $9.3\ \Omega$ to $5.6\ \Omega$).

Key Takeaways

• Brightness of a filament lamp depends on the electrical power ($P = I^2 R = VI$) delivered to it.
• Adding components in series increases total resistance and decreases current.
• Filament lamp resistance decreases when it is colder (operating at lower current).

Common Mistakes

• Stating the lamp gets brighter because the total resistance went up.
• Confusing the total circuit resistance with the individual lamp resistance.

Things to Be Careful About

• Ensure both the state (dimmer) and a valid causal reason (lower current / higher combination resistance / colder filament) are given.

Walkthrough

Using a protractor, place its center on point A with the baseline aligned along AB. Measure an angle of $30^\circ$ in the anticlockwise direction (above AB) and mark the point. Use a ruler to draw a straight line from A passing through this mark, extending it to a length of more than 10 cm (e.g. 11–12 cm). Label the end of this line C.

Key Takeaways

• Always align the center of the protractor accurately on the vertex (point A).
• Check the scale orientation: anticlockwise means rotating upwards from the horizontal line AB.

Common Mistakes

• Drawing the line shorter than 10 cm.
• Reading the wrong scale on the protractor (e.g. drawing $150^\circ$ instead of $30^\circ$).

Things to Be Careful About

• Ensure the line is drawn sharply and neatly using a sharp pencil and a ruler.

Walkthrough

1. Use a ruler to measure 4.0 cm from point A along the line AB towards B. Mark this point as D.
2. Using a set square or protractor, construct a line through D perpendicular ($90^\circ$) to AB, extending upwards until it intersects the line AC.
3. Label this intersection point as E.

Key Takeaways

• Perpendicular lines should be constructed at an exact angle of $90^\circ$ using a protractor or set square.
• Measuring distances should start precisely at the zero mark of the ruler.

Common Mistakes

• Inaccurate distance from A (not 4.0 cm).
• The line from D not being perpendicular to AB.

Things to Be Careful About

• Use a sharp pencil to ensure points D and E are precisely located.

Walkthrough

The normal is an imaginary line drawn perpendicular ($90^\circ$) to the reflecting surface at the point of incidence. Place the baseline of a protractor along the line AC with its origin at point E. Mark $90^\circ$ and draw a line (often dashed) through E.

Key Takeaways

• In optics, the normal is always perpendicular to the surface/boundary, not necessarily vertical or horizontal.

Common Mistakes

• Drawing the normal perpendicular to AB instead of perpendicular to the mirror line AC.

Things to Be Careful About

• Ensure the angle between AC and the normal is exactly $90^\circ$.

Walkthrough

1. Identify the angle $\theta$ between the incident ray line DE and the normal drawn at E. Label this angle $\theta$.
2. Measure $\theta$ directly using a protractor aligned with the normal and DE.
3. By geometry, in right-angled triangle ADE (where $\angle \text{DAE} = 30^\circ$ and $\angle \text{ADE} = 90^\circ$), the angle $\angle \text{AED} = 60^\circ$. Since the normal is at $90^\circ$ to the line AC, angle $\theta = 90^\circ - 60^\circ = 30^\circ$.
4. A measured value within the tolerance of $30^\circ \pm 2^\circ$ (i.e. $28^\circ$ to $32^\circ$) is accepted.

Key Takeaways

• Angle of incidence $\theta$ is the angle between the incident ray and the normal, not between the ray and the mirror.

Common Mistakes

• Measuring the angle between DE and AC ($60^\circ$) instead of DE and the normal ($30^\circ$).

Things to Be Careful About

• Ensure the protractor is properly centered at E.

Walkthrough

When marking points or optical pins along a ray of light, placing them close together magnifies any small error in the position of either point, causing a large angular deviation when drawing the ray. To ensure maximum accuracy, the points $P_1$ and $P_2$ must be separated by a large distance (at least 4 cm, or as far apart as possible on the paper).

Key Takeaways

• In ray tracing experiments with pins or marked points, maximizing the distance between points minimizes angular alignment error.

Common Mistakes

• Suggesting vague precautions such as "be careful" or "use a good ruler" instead of specifying the separation of the points.

Things to Be Careful About

• The marking scheme specifically looks for the distance: "at least 4 cm", "further apart", or "not close together".

Walkthrough

1. Place the center of a protractor at point Aʹ with the baseline aligned along AʹBʹ.
2. Measure an angle of $60^\circ$ anticlockwise (upwards) from AʹBʹ.
3. Using a ruler, draw a line from Aʹ through the mark, extending it to a length greater than 10 cm (e.g. 11–12 cm).
4. Label the end of the line Cʹ.

Key Takeaways

• Follow instructions carefully regarding line length and labelling.

Common Mistakes

• Drawing the angle clockwise below AʹBʹ or drawing a line shorter than 10 cm.

Things to Be Careful About

• Ensure the angle is exactly $60^\circ$ ($\pm 1^\circ$).

Walkthrough

1. Measure 4.0 cm from Aʹ along the line AʹBʹ and mark the point Dʹ.
2. Using a set square or protractor, draw a perpendicular ($90^\circ$) line to AʹBʹ through Dʹ upwards until it crosses AʹCʹ.
3. Label the intersection of this line with AʹCʹ as point Eʹ.
4. Align a protractor along line AʹCʹ at point Eʹ and draw a normal line perpendicular ($90^\circ$) to AʹCʹ.

Key Takeaways

• Keep track of which line is perpendicular to which: DʹEʹ is perpendicular to AʹBʹ, whereas the normal is perpendicular to AʹCʹ.

Common Mistakes

• Confusing the two perpendiculars (drawing the normal perpendicular to AʹBʹ instead of AʹCʹ).

Things to Be Careful About

• Ensure clean and accurate pencil lines for clear intersection at Eʹ.

Walkthrough

1. Identify the angle between the ray DʹEʹ and the normal at Eʹ, and label it $\alpha$.
2. To ensure that the normal is drawn accurately at $90^\circ$ to the mirror line:
   • Use a sharp pencil to produce thin, precise lines.
   • Use a set square or protractor properly aligned with line AʹCʹ.
   • View the protractor scale directly from above (at $90^\circ$) to avoid parallax error.

Key Takeaways

• Accuracy in graphical constructions requires sharp pencils, appropriate drawing instruments (set squares, protractors), and avoiding parallax error.

Common Mistakes

• Stating vague answers like "work carefully" or "take your time".

Things to Be Careful About

• Make sure to give a specific, practical technique accepted by the syllabus.

Walkthrough

1. Measure the angle $\alpha$ between the line DʹEʹ and the normal at Eʹ using a protractor.
2. Geometrically, in the right-angled triangle AʹDʹEʹ, $\angle \text{DʹAʹEʹ} = 60^\circ$ and $\angle \text{AʹDʹEʹ} = 90^\circ$, so $\angle \text{AʹEʹDʹ} = 30^\circ$.
3. The normal is at $90^\circ$ to AʹCʹ, so the angle $\alpha = 90^\circ - 30^\circ = 60^\circ$.
4. Any measured value within $60^\circ \pm 2^\circ$ ($58^\circ$ to $62^\circ$) is accepted.

Key Takeaways

• The angle of incidence equals the tilt angle of the mirror relative to the baseline when the incident ray is perpendicular to the baseline.

Common Mistakes

• Measuring the angle between DʹEʹ and AʹCʹ ($30^\circ$) instead of DʹEʹ and the normal ($60^\circ$).

Things to Be Careful About

• Ensure the protractor is correctly centered on Eʹ.

Walkthrough

The stopwatch display shows min : s 1/100s. The readout is 0:22:63, which means 0 minutes, 22 seconds, and 63 hundredths of a second. This is recorded as 22.63 s.

Key Takeaways

Digital stopcards read in the format min : s : 1/100s. Always include the trailing zero if the hundredths place is non-zero, but here 63 is already two digits.

Common Mistakes

Reading the display as 22.63 minutes or ignoring the hundredths column.

Things to Be Careful About

Ensure the unit is seconds (s) and the precision matches the instrument (0.01 s).

Walkthrough

The second stopwatch reading is 0:21:84, which is 21.84 s.
The average time is calculated as:

The question asks for the answer to the nearest 0.1 s, so we round 22.235 to 22.2 s.

Key Takeaways

Averages should be calculated using the full precision of the readings before rounding to the required decimal places.

Common Mistakes

Rounding the individual readings before averaging (e.g. 22.6 + 21.8 = 44.4 / 2 = 22.2, which gives the same result here but is bad practice), or rounding 22.235 up to 22.3.

Things to Be Careful About

The question specifically asks for the answer to the nearest 0.1 s. Always check the required precision.

Walkthrough

The formula for the average rate of flow is $R = \frac{30\ \text{cm}^3}{t_{av}}$. Using the unrounded average time $t_{av} = 22.235\text{ s}$ (to avoid rounding errors):

Rounding to 3 significant figures gives 1.35.
The unit is volume divided by time, which is $\text{cm}^3/\text{s}$.

Key Takeaways

When calculating derived quantities, use unrounded intermediate values to avoid cumulative rounding errors. The unit is derived from the formula: $\text{cm}^3$ divided by s.

Common Mistakes

Using the rounded average (22.2) gives $30/22.2 = 1.351$, which still rounds to 1.35, but it is better practice to use the exact value. Forgetting the unit or writing it as $\text{cm}^3\text{ s}^{-1}$ (5054 accepts both, but the slash form is standard in the paper).

Things to Be Careful About

The question asks for the unit as a separate blank. Ensure $\text{cm}^3/\text{s}$ is written clearly.