Physics 5054/32 — May/June 2024

Walkthrough

The candidate is asked to short-circuit terminals X and Y with a lead, close the switch, and record the initial readings. The voltmeter is connected in parallel across the diode, so it measures the potential difference across the diode. The ammeter is in series, measuring the total current. The candidate must read the voltmeter to at least 1 decimal place (e.g., $0.75\text{ V}$) and the ammeter to at least 2 decimal places (e.g., $0.35\text{ A}$). The mark scheme specifies acceptable ranges: $V$ between $0.60\text{ V}$ and $0.90\text{ V}$, and $I$ between $0.20\text{ A}$ and $0.40\text{ A}$.

Key Takeaways

• Voltmeters are connected in parallel across the component whose p.d. is being measured.
• Ammeters are connected in series to measure the current flowing through the circuit.
• Readings must be recorded to the precision allowed by the instrument's scale, including trailing zeros where appropriate.

Common Mistakes

• Recording the ammeter reading to only 1 decimal place (e.g., $0.4\text{ A}$ instead of $0.40\text{ A}$).
• Reading the voltmeter or ammeter incorrectly due to parallax error (not viewing the scale at eye level).
• Forgetting that the voltmeter measures the p.d. across the diode only, not the total p.d. of the power source.

Things to Be Careful About

• The mark scheme requires $V$ to at least 1 decimal place and $I$ to at least 2 decimal places. A reading like $0.7\text{ V}$ or $0.3\text{ A}$ would not score.
• The values must fall within the specified ranges ($0.60-0.90\text{ V}$ and $0.20-0.40\text{ A}$); values outside these indicate a faulty setup or incorrect instrument selection.
• Always open the switch and remove the lead before moving to the next step to avoid altering the circuit or damaging components.

Walkthrough

The candidate connects the $3.3\ \Omega$ resistor between terminals X and Y. This adds resistance in series with the rest of the circuit, so the total resistance increases and the current $I$ must decrease. The candidate records the new $V$ and $I$ readings. The ammeter reading must be less than the value recorded in part (a) (e.g., $0.25\text{ A} < 0.35\text{ A}$) and must be recorded to at least 2 decimal places. Neither reading should be zero.

Key Takeaways

• Adding resistance in series increases the total circuit resistance, which decreases the current for a constant supply voltage.
• The diode is a non-ohmic conductor; its resistance changes with current, so the voltage across it will also change, but not proportionally.

Common Mistakes

• Forgetting to open the switch before connecting the resistor, which could cause a short circuit or damage.
• Recording the ammeter reading without the required precision (2 d.p.).
• Assuming the voltage across the diode will remain exactly constant; it will change slightly as the current changes.

Things to Be Careful About

• Ensure the $3.3\ \Omega$ resistor is connected between X and Y, not in parallel or across other components.
• The ammeter reading must be strictly less than the reading in part (a). If it is not, the circuit is not assembled correctly or the resistor is faulty.
• Record readings immediately after closing the switch to avoid heating effects altering the diode's resistance.

Walkthrough

The candidate repeats the procedure from part (b) using the $6.8\ \Omega$ and $10\ \Omega$ resistors. Each time, the total resistance increases, so the current $I$ decreases further. The candidate records $V$ and $I$ for both resistors, completing the table. The ammeter readings must continue to decrease (e.g., $0.18\text{ A}$ and $0.15\text{ A}$). The voltmeter readings will also decrease slightly or remain relatively constant (diodes have a relatively flat V-I characteristic in the forward-biased conducting region).

Key Takeaways

• A good experiment requires a sufficient range of values for the independent variable (here, the resistance between X and Y) to observe the trend clearly.
• The candidate must systematically change one variable at a time and record the corresponding dependent variables.

Common Mistakes

• Failing to remove the previous resistor before connecting the next one.
• Not opening the switch between measurements.
• Recording only two sets of readings instead of all three required.

Things to Be Careful About

• Ensure the table is completed for all three resistors ($3.3\ \Omega$, $6.8\ \Omega$, $10\ \Omega$) to earn the mark.
• The current must decrease monotonically as the added resistance increases.

Walkthrough

The candidate calculates the resistance of the diode for each row using the equation $R = \frac{V}{I}$. They must substitute the recorded values of $V$ and $I$ and compute $R$, rounding to an appropriate number of significant figures (usually 2 or 3). The mark scheme also looks for the correct trend: as the current $I$ decreases (due to adding more series resistance), the calculated resistance $R$ of the diode increases. This is because the diode's resistance is not constant; it is lower at higher currents.

Key Takeaways

• Resistance can be calculated from simultaneous voltage and current readings using Ohm's law: $R = \frac{V}{I}$.
• For non-ohmic components like diodes, the resistance is not constant and depends on the current flowing through it.

Common Mistakes

• Forgetting to calculate $R$ for all four rows.
• Using the wrong values of $V$ and $I$ (e.g., mixing up rows).
• Not noticing or stating the trend that $R$ increases as $I$ decreases.
• Rounding errors in the calculation.

Things to Be Careful About

• Ensure all $R$ values are present and correct. An error carried forward (ecf) from part (c) will be accepted if the calculation $R = V/I$ is applied correctly to the (incorrect) readings.
• The trend 'R values increasing as I decreases' is a separate mark; it must be explicitly stated or clearly visible in the table.

Walkthrough

The student finds that the ammeter gives no reading when the switch is closed with X and Y shorted. The ammeter is not broken, so there is no current flowing. The circuit contains a diode, which only allows current to flow in one direction (forward-biased). If the diode is connected in reverse bias (the cathode connected to the positive terminal of the power supply), it will block the current, resulting in zero ammeter reading. Therefore, the most likely error is that the diode is connected the wrong way around. Other possible errors include the power supply or ammeter being reversed, though diode reversal is the most common and specific to this circuit.

Key Takeaways

• Diodes are directional components; they only conduct current in one direction (from anode to cathode, indicated by the arrow in the circuit symbol).
• If a diode is connected in reverse bias, it acts as an open circuit, and no current will flow.
• When diagnosing circuit faults, consider the properties of the components involved.

Common Mistakes

• Suggesting the switch is faulty or the battery is dead (the mark scheme specifically looks for a connection error with the diode, power supply, or ammeter).
• Saying 'the diode is broken' (the question implies the error is in assembly, not component failure).
• Not specifying which component is reversed (e.g., just saying 'something is reversed').

Things to Be Careful About

• The mark scheme accepts 'diode', 'power supply', or 'ammeter' connected the wrong way around. However, diode reversal is the most physically meaningful answer given the context of investigating a diode.
• Do not suggest adding a resistor or changing the voltage; the error is in the assembly direction.

Walkthrough

To ensure accurate temperature measurements, the candidate must minimize errors from temperature gradients, parallax, and heat loss. Stirring ensures the water in the test-tube is at a uniform temperature. Reading at eye level prevents parallax error on the thermometer scale. Avoiding contact with the glass prevents the thermometer from reading the glass temperature rather than the water temperature.

Key Takeaways

Accurate temperature measurements in cooling experiments require uniform temperature (stirring), correct viewing angle (no parallax), and isolation from apparatus temperatures (thermometer not touching glass).

Common Mistakes

• Stating "be more careful" (too vague, not credited).
• Saying "use a better thermometer" (does not address the technique).
• Forgetting that the thermometer must not touch the glass.

Things to Be Careful About

• The mark scheme accepts any one valid precaution. Do not list multiple unless asked.
• "Stirring" is a very strong answer because water is a poor conductor of heat, and without stirring, the top of the water in the test-tube may cool faster than the bottom.

Walkthrough

The experiment is repeated with warm water ($\sim 40 ^\circ\text{C}$) in the beaker. The hot water in the test-tube ($\sim 80 ^\circ\text{C}$) will still cool down, but the rate of cooling will be slower because the temperature difference between the hot water and the surrounding warm water is smaller than when the surrounding water was cold ($\sim 20 ^\circ\text{C}$).

Key Takeaways

The rate of cooling depends on the temperature difference between the object and its surroundings. A smaller temperature difference results in a slower rate of cooling.

Common Mistakes

• Recording temperatures that decrease faster than in the cold water (physically incorrect).
• Forgetting that the initial temperature should still be the same ($\sim 80 ^\circ\text{C}$).

Things to Be Careful About

• The third column must show a decreasing trend, but the values should be higher (closer to the initial temperature) than the second column at the same time intervals.

Walkthrough

The candidate subtracts the final temperature (at $t = 180$ s) from the initial temperature (at $t = 0$ s) for both columns. This gives the total temperature decrease over the 180-second period.

Key Takeaways

Temperature decrease is calculated as $\Delta\theta = \theta_{\text{initial}} - \theta_{\text{final}}$. This value is used to compare the rates of cooling.

Common Mistakes

• Subtracting in the wrong order (e.g., final - initial, giving a negative number).
• Using the wrong row (e.g., using the temperature at $t = 90$ s instead of $t = 180$ s).
• Forgetting to include the unit $^\circ\text{C}$.

Things to Be Careful About

• The question asks for the temperature decrease, which is a positive quantity. Ensure the calculation yields a positive value.

Walkthrough

In this practical test part, the candidate adjusts the position of the movable mass $m = 50\text{ g}$ until the metre rule balances horizontally on the pivot placed at the $50.0\text{ cm}$ mark.

The distance $d$ is measured from the pivot (at $50.0\text{ cm}$) to the centre of the movable load. Because a standard metre rule has millimeter divisions, readings must be recorded to the nearest $0.1\text{ cm}$ (or $1\text{ mm}$). Furthermore, since the rule ends at $100.0\text{ cm}$, the maximum possible distance from the pivot to the end of the rule is $50.0\text{ cm}$, so $d$ must be strictly less than $50\text{ cm}$.

Key Takeaways

• Always record metre rule measurements to the nearest $0.1\text{ cm}$ (including a trailing zero, e.g., $45.0\text{ cm}$ rather than $45\text{ cm}$).
• Check that measured values are physically possible within the dimensions of the apparatus.

Common Mistakes

• Omitting the trailing zero (e.g. writing $45$ instead of $45.0$).
• Recording the mark on the rule (e.g. $95.0\text{ cm}$) instead of the distance $d$ from the $50.0\text{ cm}$ mark.

Things to Be Careful About

Ensure the measurement is taken from the pivot position ($50.0\text{ cm}$) to the centre of mass of the slotted load, not its edge.

Walkthrough

Friction at the pivot often prevents a beam from settling into a perfect horizontal position immediately. To overcome this and locate the true equilibrium position:

1. Move the load slowly until the rule just tips downward on the right.
2. Move the load back until the rule just tips downward on the left.
3. Place the load midway between these two tipping points.

Alternatively, candidates can note the position of both outer edges of the cylindrical mass on the ruler scale and average them to find the exact centre of the mass.

Key Takeaways

• Balancing experiments require finding the sensitivity limits (the positions where tipping occurs) and averaging them.

Common Mistakes

• Giving vague answers such as "look carefully", "be more accurate", or "keep your eye level".

Things to Be Careful About

State clear, operational steps that describe how the mass is manipulated to find the balance point.

Walkthrough

To score full marks on the graph plotting:

1. Axes & Labels: The $y$-axis must be labelled with the quantity and unit ($m\ /\ \text{g}$ or $m\ (\text{g})$), and the $x$-axis with $\frac{1000}{d}\ /\ \frac{1}{\text{cm}}$ (or $\text{cm}^{-1}$).
2. Scales: The question explicitly states that axes do not need to start from $(0,0)$. Choose convenient, non-awkward scales (multiples of 1, 2, or 5) such that the plotted points span at least half the grid along both the horizontal and vertical axes.
3. Plotting: Plot all points using small crisp crosses ($\times$) or encircled dots ($\odot$), positioned within $\pm 0.5$ small square of their true values.
4. Best-fit line: Use a transparent ruler to draw a straight line of best fit with an even distribution of points on either side. The line should be thin, sharp, and drawn with a single continuous stroke.

Key Takeaways

• Scales should make plotting straightforward and use more than half the grid.
• Avoid awkward scale divisions like 3, 7, or 9 small squares per unit.
• Best-fit lines must balance points rather than simply connecting the first and last points.

Common Mistakes

• Inverted axes (plotting $1000/d$ on the $y$-axis and $m$ on the $x$-axis).
• Missing units on axes.
• Drawing thick, multiple, or "woolly" pencil lines.

Things to Be Careful About

Keep pencil lines sharp and thin. Do not force the line through the origin if the scale does not start at $(0,0)$.

Walkthrough

To find the gradient $G$ of the straight line:

1. Choose two points lying directly on the line of best fit (not data points from the table, unless they happen to lie exactly on the line).
2. Ensure the points are far apart — the mark scheme requires using at least half the length of the drawn line, meaning $\Delta m \geqslant 25\text{ g}$.
3. Indicate the coordinates or draw the gradient triangle clearly on the graph.
4. Calculate $G = \frac{\Delta m}{\Delta (1000/d)}$. The value should lie in the range $2.2 \pm 0.2$.

Key Takeaways

• Always use a large triangle ($≥$ half the line) to determine graph gradients.
• Read coordinates from the drawn line, not from raw data points in the table.

Common Mistakes

• Using a very small triangle (span of $\Delta m < 25$).
• Calculating the gradient using a single data point ($y/x$).
• Inverting the gradient formula ($\Delta x / \Delta y$).

Things to Be Careful About

Check scale readings carefully when determining $(x_1, y_1)$ and $(x_2, y_2)$ from the graph grid.

Walkthrough

The mass $M$ of the load fixed to the rule is given by the relation:

Substitute the value of $G$ calculated in part (e) (e.g. $G = 2.24$):

Accepted values for $M$ fall within $50.0 \pm 5.0\text{ g}$ (i.e. $45\text{ g}$ to $55\text{ g}$).

Key Takeaways

• Follow through carefully with your gradient value $G$.

Common Mistakes

• Arithmetic errors in multiplication.
• Forgetting to write the answer to 2 or 3 significant figures.

Things to Be Careful About

Ensure the value of $M$ is consistent with your value of $G$ from part (e).

Walkthrough

The anticlockwise moment produced by the fixed load $M \approx 50\text{ g}$ at the $5.0\text{ cm}$ mark (distance $45.0\text{ cm}$ from the pivot at $50.0\text{ cm}$) is:

To balance this with a mass $m = 40\text{ g}$, the distance $d$ needed is:

Since the metre rule ends at $100.0\text{ cm}$, the maximum possible distance from the pivot at $50.0\text{ cm}$ to the end of the rule is $50.0\text{ cm}$. A distance of $56.25\text{ cm}$ is off the end of the rule, making it physically impossible to balance the rule.

Key Takeaways

• The physical limits of experimental apparatus (such as ruler length) constrain the range of measurable variables.

Common Mistakes

• Stating vaguely that "40 g is too small" or "the mass is too light" without explaining that the balance point lies beyond the end of the rule.

Things to Be Careful About

Clearly link the mass being too small to the balance point falling beyond the $100\text{ cm}$ end of the rule.