A-level Topics

18 January

Base Unit Building Blocks

Seng Kwang Tan 01 Quantities and Measurement, IP3 01 Measurement 0 Comments

Base units are the fundamental building blocks from which all other units of measurement are constructed. In the International System of Units (SI), quantities such as length (metre), mass (kilogram), time (second), electric current (ampere), temperature (kelvin), amount of substance (mole), and luminous intensity (candela) are defined as base units because they cannot be broken down into simpler units. By combining these base units through multiplication, division, and powers, we can form derived units to describe more complex quantities—for example, speed (metres per second), force (newtons), and energy (joules).

This app teaches dimensional analysis by letting learners build derived physical quantities from the seven SI base units. Through an interactive fraction-style canvas, users place base-unit “bricks” into the numerator or denominator to form target dimensions (e.g., kg m⁻³ for density), reinforcing how exponents and unit positions encode physical meaning. Each quantity is accompanied by concise, inline hints that show the unit structure of the terms in its defining equation (for example, mass and volume in density, or force and area in pressure), helping students connect formulas to their base-unit foundations. By checking correctness and exploring more quantities (force, energy, power, electric charge, voltage, resistance, heat capacity, specific heat, latent heat, molar mass), learners develop an intuitive, transferable understanding of how physics equations translate into consistent SI units.

The app (https://physicstjc.github.io/sls/base-units/) can be directly embedded into SLS as the domain is now whitelisted.

06 December

Simulation for Series and Parallel Circuit

Seng Kwang Tan 16 Circuits, IP4 12 DC Circuits, Javascript 0 Comments
2.0 Ω
2.0 Ω
Drag the ammeter (A) or voltmeter (V) onto a bulb to attach. Ammeter measures current inline; voltmeter measures voltage across the bulb.
6V Battery Bulb 1 2Ω Bulb 2 2Ω A V

This interactive simulation helps students compare what happens in series and parallel circuits using two bulbs and a 6 V battery. Learners can switch between series and parallel configurations, adjust the resistance of each bulb, and see how this affects the current, voltage and brightness of the bulbs. By dragging the ammeter (A) into the circuit, they can measure the current through a chosen bulb, and by placing the voltmeter (V) across a bulb, they can measure the potential difference across it. The changing brightness of each bulb represents the power it dissipates, allowing students to visualise ideas such as: in a series circuit the current is the same through all components but the voltage is shared, while in a parallel circuit the voltage across each branch is the same but the currents can be different.

05 December

Simulation of electron drift speed versus temperature

Seng Kwang Tan 15 Currents, IP4 11 Current Electricity 0 Comments

Metal Lattice Simulation

3.0 V
20 °C
Mean drift speed: 0.0 mm/s
At low temperature, ions vibrate less, so collisions are fewer and drift speed (and current) is higher for 3.0 V.
Your browser does not support the HTML5 canvas tag.

This simulation demonstrates the principle that the resistance of a metal conductor increases with temperature. As temperature rises, the metal ions in the lattice vibrate more vigorously. This increased vibration causes charge carriers (electrons) to collide more frequently with the ions, hindering their movement. As a result, resistance increases and the current flowing through the conductor decreases for the same applied voltage.

At the A-Level, this simulation extends the understanding of current by examining it from a microscopic perspective in terms of mean drift velocity. Instead of viewing current simply as the rate of flow of charge, students learn that electrons in a conductor move slowly on average, with a small net drift in the direction of the electric field. The current depends on how many charge carriers are available and how fast they drift. This is expressed using the equation:

$$I = nAv_dq$$

where II is the current, nn is the number density of charge carriers, AA is the cross-sectional area of the conductor, vdv_dis the mean drift velocity of the electrons, and qq is the charge of each carrier. As temperature increases, more frequent collisions reduce the drift velocity, helping to explain why current decreases even though the charge carriers are still present—linking microscopic behaviour with macroscopic electrical measurements.

19 September

Moving charge between two charged spheres

Seng Kwang Tan 14 Electric Fields 1 Comment

This simulation is made upon request by a colleague teaching JC2 this year.

The motion of a mobile charge between two source charges is governed by Coulomb’s law ($F = \dfrac{Q_1Q_2}{4\pi\epsilon_0r^2}$) and the electric field. Each source charge produces a field in space, exerting a force on the test charge according to $F = qE$. The total field is the vector sum of all source charges, with positive charges moving along the field and negative charges moving opposite to it.

The test charge’s acceleration depends on the net force, changing its velocity and trajectory according to Newton’s second law. Its motion shows how attractive and repulsive forces combine, providing an intuitive view of electrostatic interactions and field lines.

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11 September

RC Circuit

Seng Kwang Tan 16 Circuits, GeoGebra 0 Comments
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This is meant for the A-level topic of Circuits, for which students have to describe and represent the variation with time, of quantities like current, charge and potential difference, for a capacitor that is charging or discharging through a resistor, using equations of the form $x = x_0e^{-\frac{t}{\tau}}$ or $x = x_0(1 – e^{-\frac{t}{\tau}})$, where $\tau = RC$ is the time constant.

This GeoGebra interactive by Dave Nero is well-designed. It illustrates how the charge, voltage, and current in an RC circuit change over time. You can adjust the resistance, capacitance, and supply voltage using the sliders provided. The two circuit switches can be opened or closed by selecting the check boxes. A drop-down menu allows you to choose which quantity to display on the graph, and pressing the play button in the lower left corner starts the time-dependent plot.

When a capacitor is connected in series with a resistor, the changes in current, charge and potential difference follow an exponential pattern, controlled by the time constant $\tau = RC$.

During charging, the capacitor begins with no charge, so the battery’s full potential difference appears across the resistor, giving a maximum initial current. As charge accumulates on the plates, the potential difference across the capacitor rises. This reduces the potential difference across the resistor, causing the current to decrease. The charge on the capacitor and its potential difference both increase with time according to the equation $x = x_0 \left(1 – e^{-t/\tau}\right)$, approaching their maximum values asymptotically. Meanwhile, the current decreases exponentially with time, following $x = x_0 e^{-t/\tau}$.

During discharging, the capacitor starts with an initial charge and potential difference. Once connected across the resistor, this stored energy drives a current in the circuit. As the charge leaves the plates, the potential difference across the capacitor falls. Both charge and potential difference decrease exponentially with time according to $x = x_0 e^{-t/\tau}$, and the current also decays exponentially to zero, reversing direction compared to charging.

The time constant $\tau = RC$ sets the rate of change. After one time constant, a charging capacitor reaches about 63% of its final charge, or a discharging capacitor falls to about 37% of its initial charge. After about five time constants, the process is practically complete.

11 September

Bouncing ball with energy loss

Seng Kwang Tan 03 Motion and Forces, AI, IP3 02 Kinematics, IP3 03 Dynamics, IP3 06 Work, Energy and Power, Simulations 0 Comments
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This simulation offers a clear and interactive way to explore the motion of a ball bouncing on the ground, highlighting how displacement, velocity, and acceleration change over time. On the left, you’ll see the animation of the ball with vectors showing its position (green), velocity (pink), and acceleration (blue). The sliders at the top allow you to adjust the starting height, the percentage of energy lost on each bounce, and whether air resistance is included. You can pause, reset, or let the motion run continuously, while the time slider doubles as a scrubber when the simulation is paused.

On the right, the three graphs display how each physical quantity varies with time. The position–time graph shows the ball’s vertical displacement, always measured relative to the lowest point of its center of mass. The velocity–time graph alternates between negative and positive values, reflecting the downward and upward motion during each bounce, while the acceleration–time graph remains mostly constant at –g, with spikes at the moment of collision. Together, the animation and graphs help link the visual motion with the quantitative data, reinforcing the relationships between these variables.

The underlying theory follows Newton’s laws of motion. The ball accelerates downwards under gravity until it collides with the ground, where it loses some energy depending on the restitution factor. This is why the bounce height diminishes over time. The velocity vector shows not only the speed but also the direction of motion, while the acceleration vector indicates that gravity always acts downward, regardless of whether the ball is rising or falling. By adjusting energy loss during each collision and air resistance, you can model more realistic scenarios and see how dissipative forces affect motion, making this a powerful tool to visualize the physics of bouncing objects.