## Geogebra App on Maximum Power Theorem

This simulation demonstrates the power dissipated in a variable resistor given that the battery has an internal resistance (made variable in this app as well).

Since the power dissipated by the resistor is given by

$P=I^2R$

and the current is given by

$I=E(R+r)$,

$P= E^2\times\frac{R}{(R+r)^2}=\frac{E^2}{\frac{r^2}{R}+R+2r}$

This power will be a maximum if the expression for the denominator

$\frac{r^2}{R}+R+2r$

is a minimum.

Differentiating the expression with respect to R, we get

$\frac{d(r^2/R+R+2r)}{dR}=-\frac{r^2}{R^2}+1$

When the denominator is a minimum,

$-\frac{r^2}{R^2}+1=0$, so

r = R.

## Geogebra Simulation of a Potentiometer

Some of the more challenging problems in the topic of electricity in the A-level syllabus are those involving a potentiometer. The solution involves the concept of potential divider and the setup can be used to measure emf or potential difference across a variety of circuits components. Basically, students need to understand the rule - that the potential difference across a device is simply a fraction of the circuit's emf, and that fraction is equal to the resistance of the device over the total resistance of the circuit.

$V_{device}=\frac{R_{device}}{R_{total}}*emf$

The intention of this Geogebra app is for students to practise working on their calculations, as well as to reinforce their understanding of the principle by which the potentiometer works.

## Geogebra Apps for Singapore Physics

I've curated a series of Geogebra apps that are relevant and useful for the instructional objectives under the Singapore-Cambridge GCE 'O' and 'A' level syllabi. Some of these apps were created by myself. If you have any ideas for new Geogebra apps, do let me know in the comments section below and I'll see if it's possible to create. Alternatively, if you have come across other Geogebra apps that can be relevant to the local physics syllabus, I would gladly include them into my lists!

## Box on a Vertical Oscillating Spring - Geogebra App

Students can explore how varying frequency and amplitude of the vertical oscillation of a platform could cause an object resting on it to temporarily leave the platform (i.e. when normal contact force is zero).

## PV Diagram for an Ideal Gas

Applying the 1st Law of Thermodynamics to 4 simple changes on an ideal gas, students can check their understanding using this Geogebra app. When is work done positive? Which processes bring about an increase in internal energy or temperature? Which processes require heat input?

## Geogebra App for Kinematics

As one of the first topics in A-level physics, kinematics introduces JC students to the variation of velocity and displacement with acceleration. Very often, they struggle with the graphical representations of the 3 variables.

This Geogebra app allows students to vary acceleration (keeping it to a linear function for simplicity) while observing changes to velocity and displacement. Students can also change the initial conditions of velocity and displacement.

The default setting shows an object being thrown upwards with downward gravitational acceleration of 10 m s-2.

The movement of the particle with time is shown on the left with a reference line showing the position on the displacement graph.

## Wavefront

In order to help students visualise a wavefront, a 3-D image is usually used to show the imaginary line joining particles in phase. I created the Geogebra apps below to allow students to change the wavefront and observe it move with time at a constant wave speed. There represent simplified versions of waves on a ripple tank with a linear and circular wavefront.