*July*

The Potential Divider Rule

Determining the relative brightness of light bulbs using the potential divider rule

How Internal Resistance affects brightness of light bulbs

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## How emf is induced

## Electromagnetic Induction and its Effects

the world in a different light

31 *July*

The Potential Divider Rule

Determining the relative brightness of light bulbs using the potential divider rule

How Internal Resistance affects brightness of light bulbs

30 *July*

To explain a phenomenon that happens due to Electromagnetic Induction, we can use an acronym CFILE to structure our answer.

**C** stands for **cutting of flux** or **changing of flux linkage**. This is necessary for electromagnetic induction to happen. When a wire is pulled through a magnetic field perpendicular to it, it is said to be cutting the field lines. When a magnet enters a coil of wires, we can say that the magnetic flux linkage is increasing.

**F** stands for **Faraday’s law**, which states that *the induced e.m.f. in a circuit is directly proportional to the rate of change of flux-linkage or to the rate of cutting of magnetic flux.*

**I** stands for an **induced current**. However, do note that this is only possible if there is a closed circuit or a path for the current to flow.

**L** stands for **Lenz’s law**, which *states that the direction of the induced e.m.f. is such that it tends to oppose the flux change causing it, and does oppose it if induced current flows. *

**E** stands for **effect**. This is really just stating how an induced current or Lenz’s law causes the phenomenon in question.

28 *July*

A video tutorial on the use of the Addestation datalogger with its motion sensor to measure the displacement of a bouncing ball and to observe the velocity and acceleration using its differentiation function.

28 *July*

- The
**root-mean-square**value of an alternating current is equivalent to the steady direct current that would dissipate heat at the same rate as the alternating current in a given resistor. - For a sinusoidal source,

(a) the root mean square value of the current is given by $$I_{rms}=\frac{I_o}{\sqrt{2}}$$.

(b) the mean or average power <*P*> absorbed by a resistive load is half the maximum power.

$$<P>=\frac{1}{2}P_o=\frac{1}{2}{I_o}{V_o}=\frac{1}{2}{I_o}^2R =\frac{V_o^2}{2R}$$.

- An a.c. transformer is a device for increasing or decreasing an a.c. voltage. It consists of a primary coil of
*N*_{p}turns and voltage*V*_{p}and secondary coil of*N*_{s}turns and voltage*V*_{s}wrapped around an iron core. - For an ideal transformer (assuming no energy is lost), the following equation is obeyed

$$\frac{N_s}{N_p}=\frac{V_s}{V_p}=\frac{I_p}{I_s}$$. - Power loss in the transmission lines is minimized if the power is transmitted at high voltages (i.e. low currents) since $$P_{loss}=I^2R$$ where
*I*is the current through the cables and*R*is the resistance of the cables. - The equation $$P=\frac{V^2}{R}$$ is often mistakenly used to suggest that power lost is high when voltage of transmission is high. In fact,
*V*refers to the potential difference across the cables, which often have but a fraction of the overall resistance through which the current passes.

24 *July*

[accordions autoHeight=’true’]

[accordion title=”1. Particle Nature of Light”]

- A
**photon**is a quantum of electromagnetic radiation. - The energy of a photon is given by
*E*=*hf*, where*h*is Planck’s constant (6.63 $$\times$$ 10^{-34}J s) and*f*is its frequency.

[/accordion]

[accordion title=”1.1 Photoelectric Effect”]

- The
**photoelectric effect**is the emission of electrons from a metal surface when electromagnetic radiation of sufficiently high frequency is shone on it. - The energy of an incident photon is the sum of the maximum kinetic energy $$K.E._{max}$$ of the emitted electrons from the metal surface and the work function $$\Phi$$ of the metal. Einstein’s photoelectric equation states that

$$hf=\Phi +K.E._{max}=hf_o +K.E._{max}$$

- where $$f_o$$ is the
**threshold frequency**or minimum frequency of the electromagnetic radiation below which no electrons are emitted from the metal surface regardless of the intensity of the radiation. - The
**work function**$$\Phi$$ of a metal is the minimum energy needed to remove an electron from the metal surface. - $$K.E._{max}$$ can be measured by applying a voltage to prevent the emitted electrons from reaching the electrode that collects them. This voltage is known as the stopping voltage $$V_s$$ and since the charge of an electron is
*e*, the equation can be rewritten as

$$hf=\Phi + eV_s$$.

[/accordion]

[accordion title=”1.2 Line Spectra”]

- An atom is in the ground state when its electron occupies the lowest energy level. When the atom gains energy, its ground state electron makes a transition to a higher energy level. The atom is said to be in an excited state.
- At this excited state, the electron is unstable. It will jump to a lower energy level by emitting a photon whose energy is equal to the energy difference between the two levels. The photon energy is given
*hf = E*_{higher}– E_{lower.} - The
**emission line spectra**are the spectra of light radiated by individual atoms in a hot gas when the electrons in the atoms jump from higher energy levels to lower energy levels. Each spectrum consists of coloured lines on a dark background. - The
**absorption line spectra**consists of dark lines on a coloured background. When a beam of white light is passed through a cool gas, photons whose energies are equal to the excitation energies of the gas atoms, are absorbed. These photons are re-emitted in all directions, so the intensity of these wavelengths in the transmitted white light beam is reduced.

[/accordion]

[accordion title=”2. Wave Nature of Particles”]

- Louis de Broglie postulated that, because photons have wave and particle characteristics, perhaps all forms of matter have both properties. Electron diffraction provides evidence for the wave nature of particles.
- The de Broglie wavelength of a particle is given by $$\lambda = \dfrac{h}{p}$$
*p*is the momentum (*mv*) of the particle and*h*is Planck’s constant.

[/accordion]

[accordion title=”3. X-ray Spectrum”]

[/accordion]

[accordion title=”4. Heisenberg Uncertainty Principle”]

[/accordion]

[accordion title=”5. Wave Function and Probability”]

- An electron can be described by a wave function $$\Psi$$ where the square of the amplitude of the wave function $$|{\Psi}|^2$$ gives the probability of finding the electron at a point.

[/accordion]

[accordion title=”6. Quantum Tunneling”]

- Classically, an electron of energy
*E*approaching a potential barrier, whose height*U*is greater than*E*, cannot penetrate the barrier but would simply be reflected and return in the opposite direction. - However, quantum mechanics predicts that since $$|{\Psi}^2|$$ is non-zero beyond the barrier, there is a finite chance of this electron tunnelling through the barrier and reaching the other side of the barrier.
- The transmission coefficient
*T*represents the probability with which an approaching electron will penetrate to the other side of the barrier. The transmission coefficient*T*is given by $$T=e^{-2kd}$$ where $$k=\sqrt{\dfrac{8\pi^2m(U-E)}{h^2}}$$

[/accordion]

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19 *July*

This video tutorial is a guide for next week’s practical for CG18/12.