Key areas A.C as a current which changes direction and instantaneous value with time Calculations involving peak and r.m.s. values Determination of frequency from graphical data

What we will do today: Revise the two types of electrical current, a.c. and d.c. Give examples on peak voltage, Vpeak, and peak current, Ipeak.

Background revision (a.c. and d.c.) There are two types of electrical current: Direct Current (d.c.) where the current only travels in one direction eg a battery. Alternating Current (a.c.) where the current is constantly changing direction eg the mains socket.

Background revision – oscilloscope An electronic device called an oscilloscope can be used to draw a graph of the electrical signal of both a.c. and d.c. a.c d.c (above AND below) (above OR below)

Using an oscilloscope Oscilloscopes have dials on them to allow you to calibrate two things about the signal produced: On the x-axis – time per cm (time base often given in ms) On the y-axis – volts per cm (voltage gain often given in mV)

Period of a wave The period of a wave is the time taken for one complete wave to pass a point. It has the symbol T and is measured in s. For example, if we have an oscilloscope set to 1ms cm-1 (a time of 1ms for each gridline 1 cm apart) as shown:

Then we can see that one complete wave is made after 4 boxes. Therefore the period of 1 wave, T = 4 x 1ms = 4ms: T = 4 x 10-3 s

Measuring the Frequency of a wave Once we have established the period of a wave, T, we can find the frequency of a wave, f, by the equation: f = 1 T

Measuring the Frequency of a wave Frequency on signal generator (Hz) Period of one wave, T (s) Frequency calculated [f = 1 / T ] (Hz)

Definition of Peak (read) When an athlete is at their “peak”, we say they are at their absolute best. Will an athlete always be at their peak in every performance? No! Therefore, peak is the absolute maximum!

Peak Voltage When we consider voltage there are two values that we must consider: Peak voltage R.m.s. voltage (root mean square voltage) Peak voltage is “always bigger” than r.m.s. voltage The value quoted for the mains (230V) is the r.m.s. value. The r.m.s. voltage of an a.c. value is equivalent to the d.c. value e.g. an r.m.s of 230V a.c = 230V d.c.

Peak voltage Oscilloscope traces show the peak voltage of a wave, consider the following oscilloscope trace: (the y-gain setting is set to 0.1 V cm-1) The amplitude shown is 2 cm. Therefore the peak voltage is 2 x ‘volts per cm’ setting on the control. 2 x 0.1v cm-1 = 0.2 V

Peak and r.m.s.formulae The peak voltage and r.m.s. voltage are related by: Vpeak = √2 Vr.m.s Peak current and r.m.s current have a similar relationship: Ipeak = √2 Ir.m.s

2004 Qu: 12

2005 Qu: 9

2007

2003 Qu: 25

Past Paper 2000 Qu: 26(a) 2006 Qu: 26(a)

What we will do today: State what is meant by Total Internal Reflection and the Critical Angle. State the relationship between the refractive index and the critical angle. Carry out calculations on the above.

Total Internal Reflection and Critical Angle

Revision from last day sin θ1 / sin θ2 = λ1 / λ2 = v1 / v2 n = sin θ1 / sin θ2 We can express this as: n2 / n1 = sin θ1 / sin θ2 NB The refractive index of air is 1.

Experiment Draw round a semi-circular block. Draw in the normal line through the centre. Shine a light ray along the normal to the centre of the block. Continue to shine light ray at the centre and slowly move the light ray outwards (diagram 1). Keep going until the angle of refraction is 900 (diagram 2). Measure the angle of incidence at this point.

Total Internal Reflection Diagram 1 – light is refracted. Diagram 2 – Light is refracted at 900, the angle of incidence in this case is called the critical angle, Θc Diagram 3 – Any angle bigger than the critical angle will show Total Internal Reflection

The Critical Angle The critical angle,Θc is the angle of incidence when the angle of refraction is 900. It is the smallest angle of incidence above which Total Internal Reflection occurs. It is often given the symbol, Θc

Total Internal Reflection Takes place when all of a light ray is completely reflected and none of it is refracted. This takes place at angles above the critical angle, Θc

Curved Surface Note that there is no refraction at the curved surface because a radial ray strikes the surface at normal incidence (i.e. perpendicular - 90º). This is why a semi-circular block is used to find the critical angle.

Uses of Total Internal Reflection Total internal reflection is used to send light signals along optical fibres. This can be used to send telecommunications such as internet, TV and phone. This is how Virgin Media provide their services.

Critical Angle and Refractive Index sin θc

Example n = 1 sin Θc n = 1.4 Θc = ? 1.4 = 1 sin Θc = 1 1.4 1.4 = 1 sin Θc = 1 1.4 Θc = (sin-1) 1 Θc = 45.6o n = 1.4 Θc = ?

Questions Complete questions 6 – 11 from section 6: Refraction of Light in class jotter

2008 Qu: 16

2009 Qu: 15

Old Higher Past Paper Questions 2001 Qu: 27(b) 2002 Qu: 27 2010 Qu: 28(b)

2001 Qu: 27(b)

2002 Qu: 27

2002 Qu: 27

Revised Higher Past Paper Questions

2014 Qu: 15

Revised Higher Past Paper Questions