Electricity

Resistance and current revision When a wire is long the resistance is high When a wire is thin the resistance is high. This means the current is low. Remember your rules for series and parallel

Series or parallel? IT = I1 = I2 = I3 = … VT = V1 + V2 + V3 + … RT = R1 + R2 + R3 + … IT = I1 + I2 + I3 + … VT = V1 = V2 = V3 = … _1_ _1_ _1_ RT = R1 + R2 Series Parallel

Potential Dividers Potential divider (or voltage divider) circuits are constructed using two or more resistors in series. I R1 R2 V1 V2 When current passes through each resistor a voltage is dropped.

From Ohm’s law V1 = I R1 V2 = I R2 So R1& R2 are in series, so the current I is the same in each. Therefore

Another variation of this equation may be used. VS Very often the resistors in a potential divider circuit will be drawn in a vertical arrangement with a power supply. The same rule still applies. Also remember VS = V1 + V2

Power Equivalence P= E t But W=QV So P= QV t But I = Q/t P=IV

We know P=IV But we also know V=IR Substituting for V P=I x IR

Power equivalence We know P=IV but we also know I=V/R Substituting for I P=V x V/R

Internal resistance In standard grade when you set up the experiment below what did you notice about the reading on the voltmeter compared to the supply? The reading on the volt meter appeared less than the supply. We had lost some volts V

The reading across the resistor is called the terminal potential difference. (t.p.d) The fact that we lose some volts means that there must be another resistor somewhere in the circuit (remember Vs= V1 +V2) The other resistor is the supply. This has an internal resistor. The resistor out with the supply is called the load resistor

We see that he t.p.d is less than the e.m.f E.m.f = p.d across R + p.d across r Bur we know V=I X R So E.m.f = I X R + I x r E= IR + Ir r R V E=I (R+r) Lost volts emf t.p.d See virtual physics for worked example

Short and Open circuits In a short circuit the load resistor has a value of 0 (connecting a wire across the battery terminals). This means E= Ir +IR becomes E = Ir In an open circuit (removing the load resistor) I = 0. This effectively means that any Vt.p.d measure is equal to the emf.

Measuring E and r r If we vary the resistance of the variable resistor we can see that as the Vtpd decreases the lost volts increases. If we measure the current also we can plot a graph of Vtpd vs I R V Vtpd current

We can see that it is a negative gradient To find the e.m.f and the internal resistance we rearrange the equation E= IR +Ir where IR is the Vtpd Vtpd = rI +E m= CHANGE IN Y CHANGE IN X So we can find the emf by extending the line back Vtpd Any we can find the internal resistance from the gradient y = m x + c current We can find the short circuit current by extending line

Wheatstone bridge This a potential divider circuit. We can find V across any resistor using out potential divider equation. Adding another potential divider across the bottom gives us a Wheatstone bridge. R1 R2

I2 R1 I2 R2 I1 = R3 I1 = R4 R1 R3 R2 = R4 V = VR1 + VR2 =VR3 + VR4 If we assume that VR1 = VR3 and VR2 = VR4 From V=IR This gives I1R1 = I2R3 and I1R2 = I2R4 This rearranges to give: I2 R1 I2 R2 I1 = R3 I1 = R4 R1 R3 R2 = R4 R1 R4 R3 R2 V I1 I2 P V Q If VR1 = VR3 and VR2 = VR4 then the p.d across points P and Q = 0V and the bridge is said to be BALANCED

R1 R4 R3 R2 V I1 I2 R1 R2 Now see virtual Physics worked example R3 R4

Unbalanced Wheat stone bridge If the resistors on a wheatstone bridge are changed then the voltmeter reading is not 0V and the bridge is out of balance. This change in p.d. and in R can be plotted on a graph to show a linear relationship. Note that a graph of I vs ΔR can also be plotted. As it is linear also I/ ΔR =CONSTANT This can be used to find other values ΔV (V) I (A) ΔR (Ω) ΔR (Ω) Note that this is only for small changes in R. If the change is over 10% then the relationship is no longer linear.

Note that is one of the resistors on the bridge is changed to a thermistor the bridge can be used to monitor temperature. Lets look at an unbalanced example

a.c and d.c. In an a.c. supply the drift velocity of the current changes direction many times a second. In d.c. drift velocity of the electrons is on one direction only. The mains supply is a.c. as it is easier to generate and distribute than d.c Lets look at how they are represented on an oscilliscope.

Period and Frequency Period The period of a wave is the time it takes for one complete wave to pass a point and it is measured in seconds (s). Frequency The frequency of a wave is the number of waves to pass a point in one second and it is measured in hertz (Hz). Period and Frequency The period and frequency of a wave are related by the equation;

Calculating period and frequency The oscilloscope below shows a waveform. The time per division and volts per division are given on the dials. Calculate the period of the waveform and then the frequency. Period of 1 wave = 5 divisions = 5 x 30 x 10-6 = 150 µs Amplitude = 3 x 60 x 10-3 = 180 mV

Worked example 1 Period of 1 wave = 1 divisions = 1 x 50 x 10-6 = 50 µs Amplitude = 3 x 30 x 10-3 = 90 mV

Worked example 2 Period of 1 wave = 10 divisions = 10 x 70 x 10-6 = 700 µs Amplitude = 3 x 40 x 10-3 = 120 mV

Worked example 3 Waveform 3, a 200Hz wave with amplitude of 8mV. Say 2 waves on screen Period of 1 wave = 5 divisions Time/Div = 0.005/5 = 1ms Say two boxes high Amplitude = 8 mV = 2 x 4 x 10-3

Worked example 4 Waveform 3, a 2kHz wave with amplitude of 0.12V. Say 1 waves on screen Period of 1 wave = 10 divisions Time/Div = 0.0005/10 = 50µs Say 4 boxes high Amplitude = 0.12V = 120mV = 4 x 30 x 10-3

Measuring frequency from oscilloscope 5 4 2 5 10 ms per div 10 2 6 2 ms per div ms per div

Frequency and current The frequency of an a.c. supply in a resistive circuit does not affect the current.

Voltage measurements Peak r.m.s

Peak Voltage An a.c. voltage applied to an oscilloscope will display a waveform. This because the voltage is constantly changing in value and also pushing forward and reverse in a cycle. There are a few ways that we can measure this type of voltage.

Measuring Peak Voltage height The peak voltage is a measure of the maximum voltage that the a.c supply provides. VP = height x v-gain e.g. for the trace shown the vertical height is 4 div and the v-gain is 2 v/div 1 2 3 V-gain VP = 2 x 4 = 8v

Calculating Peak and Rms Vp=Vrms x √2 Ip=Irms x √2 P=IV Pp = Ip Vp Prms = Irms Vrms

+ - Capacitance Electrons flow from the negative terminal to positive terminal They cannot pass through the gap on the plate and pile up on the right hand side making the plate neagtive This repels electrons on the left-hand plate making that one positive As the plate becomes more charged it is difficult for the supply to push more electrons on to the negative plate There is no more current flow supply The switch can now be opened and the capacitor will remain charges. It can be discharged by connecting a wire across the plates.

+ - Capacitance If we measure the voltage across a capacitor as it is charging we find that When its discharged (no charge on the capacitor) the voltage is zero The voltage will rise until the voltage across the capacitor is equal to the voltage supply. (Capacitor is fully charged) We can plot a graph of voltage across the capacitor vs charge on the capacitor

Where C is the capacitance of the capacitor in Farads (F) We find that Q α V So Q/V=Constant We can say C = Q / V Where C is the capacitance of the capacitor in Farads (F) This means the number of coulombs a capacitor can store per volt. Q (C) Vc (V) Now look at virtual physics to see the effects of charging and discharging a capacitor in series with a resistor.

Resistance in a capacitor circuit + - Charging Vc t supply I Discharging I Vc t t t Now look at virtual physics to see how the size of a resistor effects charging.

Energy In a capacitor Work is done to move electrons onto the plates of a capacitor. This can be found by finding the area under the QV graph E= ½ l x b E = ½ QV Q (C) V (v)

By substitution C= Q/V into E= ½ QV The energy stored by a capacitor can also be found by E= ½ CV2 And E = ½ Q2 / C Look at virtual Physics for your worked example.

Current and Frequency in a capacitor A capacitor charges and discharges at the frequency of its supply. In a capacitive circuit the current is directly proportional to the frequency. I (A) F (hz) Look at virtual physics for some uses of capacitors

Smoothing in a full wave rectifier. (used to change a.c. to d.c.) Input voltage Output voltage

Blocking DC in a circuit. (isolating dc in an amplifier circuit from the microphone) Output voltage Input voltage

Storing charge in a flash lamp. (photography)

Switching circuits Describe how the circuit works to light the LED. Under what conditions will the LED light? Vs R

The transistor An electronic switch which allows a current to flow (conduct) through the collector when the voltage across the base and transistor is high enough. Around 0.7V Collector Base Emitter

MOSFET Another type of transistor is an n-channel MOSFET transistor. This will switch on above a certain voltage. Gate Drain Source

ATOMS Electrons in atoms are contained in energy levels (bands) separated by gaps. These “bands” can only hold so many electrons. When a band is full the level above it begins to fill. The highest “full” level is called the valence band. The first unfilled band above the valence band is called the conduction band. The space between is called the band gap.

Classifying materials Using their electrical properties, we can divide materials into three groups: Conductors Semiconductors Insulators

Insulators In an insulator the highest occupied band is the valence band the gap between the valence band and conducting band is large and at room temperature there isn’t enough energy to move electrons from the valence band to conduction band. The valence band is full. The conduction empty. As a result there is no electrical conduction. Resistivity in the range of 109 m. E.g. Plastic, glass and wood. Resistivity is defined as the resistance in the wire, multiplied by the cross-sectional area of the wire, divided by the length of the wire.

Resistivity in the range of 10-9 m. Conductors In a conductor the highest occupied band is not full (The valence band and conduction band overlap) and electrons are therefore free to move in it. Resistivity in the range of 10-9 m. All metals and semi-metals like graphite, antimony and arsenic. Resistivity is defined as the resistance in the wire, multiplied by the cross-sectional area of the wire, divided by the length of the wire.

Semiconductors A semiconductor is similar to an insulator but at room temperature the gap between the valence and conducting band is smaller. This means some electrons are able to move from the valence band to conduction band allowing electrical conductivity. Increasing temperature increases this conductivity. Resistivity in the range of 101 m. E.g. Silicon (Si), germanium (Ge), selenium (Se); compounds like gallium arsenide (GaAs) and indium antimonide (InSb).

http://www. optique-ingenieur http://www.optique-ingenieur.org/en/courses/OPI_ang_M05_C02/co/Contenu_02.html

Doping The addition of an impurity like this is called doping. For ex adding arsenic to a semiconductor with only 4 electrons in its outer shell. Arsenic has 5 outer electrons. 4 of these would fill the valence band of the semiconductor. The remaining electron would occupy the conduction band.

N Type Doping In an n-type semiconductor the doping ensures there are extra electrons and most conduction is by the movement of free electrons, which are, of course, negatively charged. There is an extra layer of electrons added to the band gap at high energies between the conduction and valence band. This makes the conduction band bigger decreasing the band gap. In n-type material there are electron energy levels near the top of the band gap so that they can be easily excited into the conduction band Electrons can be elevated to the conduction band with the energy provided by an applied voltage and move through the material. The electrons are said to be the "majority carriers" for current flow in an n-type semiconductor.

P-type doping In a p-type semiconductor the doping ensures there are less electrons and most conduction takes place by the movement of electrons into these spaces (sometimes called holes). The addition of acceptor impurities contributes hole levels low in the semiconductor band gap. This makes the valence band bigger decreasing the band gap. So that electrons can be easily excited from the valence band into these extra valence levels, leaving mobile holes in the valence band Electrons can be elevated from the valence band to the holes in the band gap with the energy provided by an applied voltage. Since electrons can be exchanged between the holes, the holes are said to be mobile. The holes are said to be the "majority carriers" for current flow in a p-type semiconductor

P-n junction When a semiconductor is formed so that one half is p-type and the other half is n-type, it is called a p-n junction diode.

Depletion layer (band bending) When the p and n types are joined electrons migrate from the n-type to the p-type and holes go from the p-type to the n-type. They reach equilibrium. This creates an area where there are no free charge carriers that is an insulator. This is called the depletion layer.

Potential barrier The overall charge of the junction is neutral but electrons moving into the p-type area have made it negatively charged and holes moving into the n-type area have made it positively charged. This creates a small potential difference across the depletion layer.

No current can flow across the depletion layer unless there is enough voltage to overcome the small potential difference across the depletion layer. about 0.7 V in silicon

Graph of variation of current with p.d. across a p-n junction. V

Biasing the diode To bias a semiconductor device means to apply a voltage to it. A diode may be biased in two ways. reverse-biased or forward-biased

Reverse Bias In the reverse-biased diode the applied voltage increases the depletion layer by increasing the size of the potential barrier. The p side is made more negative, making it "uphill" for electrons moving across the junction. The conduction direction for electrons in the diagram is right to left, and the upward direction represents increasing electron energy. This creates a voltage across the depletion layer. The maximum voltage that the diode can withstand is called the breakdown voltage.

Reverse-biasing the diode makes it even less likely to conduct Reverse-biasing the diode makes it even less likely to conduct. (Although in reality a tiny current called the leakage current passes through the diode.) In reverse-bias, n-type to positive and p-type to negative.

Forward bias A voltage is applied that is greater than the potential barrier. The p side is made more positive, so that it is "downhill" for electron motion across the junction. An electron can move across the junction and fill a vacancy or "hole" near the junction. It can then move from vacancy to vacancy leftward toward the positive terminal, which could be described as the hole moving right. The conduction direction for electrons in the diagram is right to left, and the upward direction represents increasing electron energy. .

This gives the electrons from the n-type enough energy from the battery to cross the depletion layer and flow through the junction and round the circuit. The diode conducts because the depletion layer has been removed.

The diode conducts because the depletion layer has been removed The diode conducts because the depletion layer has been removed. In forward-bias, p-type to positive and n-type to negative.

LED (will always be connected with R) Electrons move from conduction band in n-type to conduction band in p-type. They then fall to valence band in p-type and emit a photon of energy.

Photodiode The p-n junction can be presented in a transparent coating. This allows photons of light to be absorbed and allow electrons to “jump” from the valence band to conducting band. The photodiode can be used in: photovoltaic mode or photoconductive mode.

Photovoltaic mode In this mode the diode has no bias voltage applied. The greater the intensity of light (more photons) the more electrons move to the conduction band and therefore a higher voltage. This is the basis of solar cells.

Photoconductive mode In this mode the photodiode is connected in reverse bias. If no light it will not conduct (as usual). However, light shining on the junction will release electrons so creating a number of free charge carriers in the depletion layer. This reduces the resistance and enables a current to flow. (The leakage current is directly proportional to the light intensity, and independent of the voltage across the depletion layer.)

Photoconductive - LDR The photodiode acts as a light dependent resistor (LDR).

Summary p-n junction diode forward bias – conducts. reverse bias – does not conduct. LED forward bias – conducts and emits light as electrons fall from conduction band to valence band. reverse bias – does not conduct, so does not emit light. photodiode no bias - photovoltaic mode – acts like a solar cell. reverse bias – photoconductive mode – acts like an LDR.

NPN transistor Applying a +ve voltage to the p-type region with respect to the n-type region causes a small current to flow.

Again applying a +ve voltage to the p-type region causes a small current to flow from the 1V terminal and a large current to flow from the 5V terminal.

MOSFET Metal Oxide Semiconductor Field Effect Transistor The three terminals are called the gate, the source and the drain. The broken line in the symbol indicates that there is normally no conducting path between the source and the drain.

How MOSFET works d made positive with respect to s – no current g made positive – attracts electrons to area under g current now flows between s and d 1 reverse bias diode so no current 2 free electrons provide path for current

Uses of transistors The MOSFET can be used as a switch with a voltage at the gate on or off. Or as an amplifier were the size of the current from source to drain depends on the amount of electrons under the oxide layer which depends on the gate voltage.

MOSFET vs npn transistor npn bipolar transistor – current controlled switch very small current from base to emitter MOSFET – voltage controlled switch zero current from gate