A-level Topics

06 December

Simulation for 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.
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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.

11 September

Dropping with air resistance

Seng Kwang Tan 03 Motion and Forces, IP3 02 Kinematics, Javascript 0 Comments
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This simulation lets you watch two equal-size spheres (light and heavy) fall, while you see their free-body diagrams (FBDs) and a velocity–time graph update in real time.

Press Start to run and Pause to discuss a moment in time. Reset restarts from rest. Use Zoom to read the force vectors clearly. Toggle Air Resistance to compare an idealised fall (no drag) with a more realistic one (drag on). The small info panel shows the current speeds and, when drag is on, each sphere’s terminal velocity.

What to look for

  • Without air resistance: Each FBD shows only weight downward. Acceleration is constant at ggg, so the velocity–time graph is a straight line from the origin for both spheres (same slope, because mass doesn’t matter when no drag acts).
  • With air resistance: A drag arrow appears upward and grows with speed. The heavy sphere’s velocity rises faster at first (its weight is larger), but both curves flatten as drag increases, and the acceleration vector shrinks toward zero. Dotted segments indicate when the two curves overlap closely.

Theory in one breath

In air, we model drag as proportional to speed: $F_\text{drag}=kv$

Net force is $ma=mg−kv \quad\Rightarrow a=g−\dfrac{k}{m}v$

As v grows, the term $\dfrac{k}{m}v$ eats into $g$, so acceleration falls.

Terminal velocity happens when forces balance: $mg=kv$​, so $v_t=\dfrac{mg}{k}$

Heavier mass ⇒ larger $v_t$​. That’s why the heavy sphere ultimately settles at a higher speed and takes longer to level off. With drag off, the model is simply $a=g$ and $v=gt$.

How to teach with it (fast)

  1. Start with Air Resistance off: Pause after a second—ask why both lines match and why only weight appears on the FBDs.
  2. Turn Air Resistance on: Run, then pause midway. What changed in the FBDs? Why is acceleration smaller now?
  3. Let it run until the acceleration vectors nearly vanish: connect “flat graph” with “balanced forces,” then read off different terminal velocities.

That’s it: start, pause, notice which vector changed, and link the picture to the equation.