2 SENSINGBasic electrical relations

• Review equations relating charge, voltage, current and power

• Understand how ion beams can be used in micromachining

A human hair with holes drilled in it by a laser beam

Part of a miniature electric motor, compared for scale with a human hair

Micro-machined structures

Part of a silicon pressure sensor, made by depositing layers and then etching material away chemically.

Silicon nitride bridging strips over a channel, forming part of a sensor to measure flow rates. Circuitry is also built into the device as it is made.

Micro-machined structures

Machining using Ion Beams

Argon ions are made by firing electrons at argon atoms. The ions are then accelerated towards a negatively charged grid to create a beam of fast moving ions. This beam of ions is directed at the material to be machined and knocks atoms out of the material, the shape of the material produced depends on the angle of the beam. This technique can be used to produce sharp diamond tips as small as 0.1μm across, mechanical polishing techniques can only produce tips 5μm across.

Ion Beams

Key facts:• Beam carries energy (its moving).• When moving particles knock into things they deliver some of their energy to the target.• Beam carries an electric current as the particles are charged and moving.•Beams are accelerated by a potential difference acting on the ions....

Show demo: 80S difference between ion beam and current in a wire.

Potential difference

For charged particles to move they need other charged particles repelling or attracting them.

Current, A

P.D. , V

Ohm’s lawProvided the temperature is constant, the

current through an ohmic conductor is directly proportional to the voltage across it.

Potential difference (voltage)The energy converted per unit

charge moving.

V = ΔE/ΔQV- Potential difference (volts)ΔE – energy (joules)ΔQ – charge (coulombs)

The basic equations

Symbols and unitsQ = charge (coulomb

C)

I = current (ampere A)

V = potential

difference (volts V)

E = energy (joule J)

P = power (watt W)

t = time (second s)

More equations

Q1. (a) 50 Coulombs of charge flow through an ammeter in 10 seconds? What is the current as measured by the ammeter?

(b) The charge on a single electron is 1.6 x 10-19 C. Use this information and your answer to Q 1(a) to work out the number of electrons that pass through the ammeter every second.

How many electrons flow out of a battery in one minute, if the current is 0.2 A?

Take the charge on an electron, e = 1.6 x 10-19 C

Sensors

• Investigate the properties of a range of sensors

Q1. What happens to the resistance of the thermistor when the temperature increases?

Q2. What happens to the current that flows as a result of this change?

Q3. What happens to the potential difference across the resistor as a result of this change in current? (Hint: V = IR)

A potential divider

Voltage in an electrical circuit

Use different models to improve yourunderstanding and your ability to explain the

role of voltage in an electrical circuit

Models to be used: treadmill model

What does each element in this circuit model represent?

How would you model the effect of increasing the battery voltage?

What effect would this have on what happens in the circuit?

Questions to really test your understanding of voltage

1. Explain what controls how fast the charges move around the circuit.

2. What happens to energy in the circuit?3. Explain how energy is related to charge and voltage.4. Why is the first bulb not brighter than the second?5. Why does a voltmeter have to be placed in parallel?6. Explain in words why the power is equal to the current

multiplied by the voltage.

Work in pairs, take it in turns to answer the questions, with the listener forcing the other person to explain properly… “what do you mean by the word…..”, “does that mean that….?”, “so how does the…”, “what would happen if…?”

Active and passive sensors

Active sensors are sensors that transmit some kind ofenergy ( microwave , sound , light , .... ) into theenvironment in order to detect the changes that occuron the transmitted energy . That means it transmits anddetects at the same time .

Passive sensors don't transmit energy but only detectsthe energy transmitted from an energy source.

The basic equations

Symbols and unitsQ = charge (coulomb

C)

I = current (ampere A)

V = potential

difference (volts V)

E = energy (joule J)

P = power (watt W)

t = time (second s)

More equations

Series and parallel resistance

• Determine rules for equivalent resistance and conductance in series and parallel circuits

CH 2 - Sensing Conductance and resistance

CH 2 - Sensing In series...

• Potential difference adds up in series• Current same for both• Resistances add up

CH 2 - Sensing In parallel...

• Currents add up• Potential difference same for both• Conductance add up• Reciprocal of resistances add up

CH 2 - Sensing Have a go...

For each of the following find the current drawn from the power source:-

CH 2 - Sensing Have a go...

Find I for this one!

Electrical power

• Derive and use equations for power dissipation in electric circuits

Starter:If a train delivers 10 wagons of coal every hour to a power station, which burns the coal, and each wagon contains 50 tons of coal, what is the rate at which coal is burned in the power station?

How do the three variables in this example relate to the electrical quantities current, potential difference and power?

Variable Electrical equivalent

Unit

Rate at which wagons arrive at power station

Current (charge passing per second)

C s-1 = A

Coal per wagon

Potential difference (energy per coulomb of charge)

J C-1 = V

Rate at which coal is dumped at power station

Power (energy per second)

J s-1 = W

Power = P.D. x Current

P = V x I

W = V x A

J s-1 = J C-1 x C s-1

By combining the equations P = V I and R = V / I,and eliminating the appropriate variables, can you obtain:

(a) An expression for P in terms of I and R (no V) ?

(b) An expression for P in terms of V and R (no I) ?

We know equation: P = IVThere are two other equations we

can get for power from this. (hint use R = V/I)

CH 2 - Sensing Have a go...

What is the power dissipated in the 5Ω resistor?

What is the power dissipated in the 12Ω resistor?

Don’t forget your the resistance rules!

CH 2 - Sensing Have a go...

Don’t forget your the resistance rules!

Find the power dissipated in each resistor and the total power of the circuit.

Current-voltage relationships

• Investigate and explain current-voltage relationships for a range of components

CH 2 - Sensing

Current, A

P.D. , V

Ohm’s lawProvided the temperature is constant, the

current through an ohmic conductor is directly proportional to the voltage across it.

Recap of - Ohm’s Law

R = V/I is a statement of Ohm’s law

CH 2 - Sensing On computers....

Instructions:Working in pairs or on own work through the following software activities on :- (You will need paper to answer the questions)Activity 160S ‘Conductance and resistance in a filament lamp’Activity 170S ‘Conductance and resistance in a neon lamp’Activity 180S ‘Conductance and resistance in a silicon diode’Activity 190S ‘Conductance and resistance in an ohmic resistor’

CH 2 - Sensing

I (A)

V (V)

I-V graphs

What do the I-V graphs look like for a filament lamp, a neon lamp, a silicon diode and an ohmic resistor? And why do they look like they do?

?

CH 2 - SensingI-V graphs

Diodes behave like ohmic resistors when the current is travelling through them in the correct direction. However, if the current is reversed the resistance of the diode is extremely high.

The temperature of a filament lamp increase as current increases. Increasing temperature increases resistance.

CH 2 - SensingI-V graphs

Ohmic resistor

Obeys ohms law completely!

Neon lamp shows non-ohmic behaviour.

The potential divider

• Investigate and explain the resistance-voltage relationship for potential divider circuits

CH 2 - Sensing

A potential divider

R1

R2

Vin

Vout

Remember potential differences divide in

series in same ratio as the resistances

211RR

RVV

in

out

CH 2 - SensingA potentiometer

Used to control a potential difference.

CH 2 - Sensing

A chain of resistors

CH 2 - Sensing

Rotary types

CH 2 - Sensing Questions 170S...A series circuit is connected as shown in the diagram.1.What is the potential difference between A and B?

2.An additional resistor of 100 ohms is connected in series between the 50 ohms resistor and the cells. What is the potential difference between A and B now?

3.The additional 100 ohms resistor is now connected in parallel with the first 100 ohms resistor. What is the potential difference between A and B now?

4.A potential divider is made from a 4 kilohm and a 6 kilohm resistor connected in series with a 20 V supply. Draw a diagram of the arrangement. What three values of potential difference can be tapped off?

CH 2 - Sensing Questions 170S cont...5. A student puts a 12 ohms variable resistor in series with a 6 V battery, expecting to get a variable potential difference.

The voltmeter is a high resistance digital multi meter. Explain why the circuit won't work. Draw a circuit which would work.

6. B is the wiper of a 100 ohms rotary potentiometer.

What is the full range of the potential difference that can be tapped off between A and B?

EMF and internal resistance

• Explain the meaning of these terms

• Measure EMF and internal resistance for a 1.5 V dry cell

CH 2 - Sensing Batteries have resistance

Resistance comes from electrons colliding with atoms and losing energy. This happens inside the battery as well as rest of circuit.

Internal resistance

Load resistance (R)

CH 2 - Sensing Batteries have resistance

Internal resistance (r) - resistance of the power source.Load resistance (R) - Total resistance of all components in rest of the circuit.

Internal resistance (r)

Load resistance (R)

CH 2 - Sensing Electromotive force (EMF)

Internal resistance (r)

Load resistance (R)

Note: It’s not actually a force!

A

V

EMF (ε) – Amount of electrical energy the battery produces for each coulomb of charge (measured in volts).

V = ε - Ir

CH 2 - Sensing Key equations

V = ε – Ir ε = I(R + r)V = ε - v ε = V + v

Where:ε – emf I - currentR – load resistance (external)r – internal resistance V – terminal p.d. v – ‘lost’ p.d.

Only this one on formula sheet!

Low and high internal resistances

Equation of straight line: y=mx+c

Use the graph toestimate the EMF andinternal resistance forthe battery.

What would the graph looklike for a battery of higher internal resistance?

Explain why the p.d. across theload resistance falls as the current increases.

High resistance source

Internal resistance and emf

Outputemf E

Rinternal

Open circuit Circuit with load Rexternal

Almost no internal resistancePotential difference V is almost equal to E

Source:Very low resistancee.g. car battery

V = I Rexternal ~ E~

ERexternal + Rinternal

I =

very small outputRinternal 0~~ Rexternal

Low resistance source

Digital thermometer• Build and test a digital

thermometer using a potential divider and thermistor

• Determine its sensitivity and resolution

Starter: Draw a potential divider circuit containing a variable resistor, thermistor and voltmeter that will give a voltage output that increases with increasing temperature. Assume that the thermistor’s resistance goes down with increasing temperatureHow would you determine the best resistance setting for the variable resistor?

A temperature sensing circuit is set up with a 6.0 V battery of negligible internal resistance, a thermistor and a fixed resistor as shown.The resistance of the thermistor in the range 10 - 100 oC is given by : R (Ω) = 4000 T (oC)

Q1. Calculate the thermistor resistance at 10 oC and 100 oC.

Q2. Which of the following would be the best choice for the fixed resistor, 300 kΩ, 300 Ω or 3 Ω? Explain your answer.

Q3. Calculate the output voltage when the temperature is 55 oC, if a 500 Ω fixed resistor is used.

Q4. It is desired to have an output voltage of 4.0 V when the temperature is 20 oC. Calculate the thermistor resistance at this temperature and hence determine the size of the fixed resistor required in this case.

A piezoelectric crystal generates voltages in response to applied stress. The maximum voltage that can be generated is 100 mV, and the crystal has an internal resistance of 1 MΩ.

Which of the following is the most suitable voltmeter for measuring the voltage generated by the crystal? Give reasons for your choice.(Hint: Draw the circuit, or see p44 of textbook)

(A) Moving coil meter with a full scale deflection of 0.5 V and an internal resistance of 200 Ω.

(B) Digital voltmeter with full scale reading of 10 V and internal resistance of 1000 Ω.

(C) Digital voltmeter with full scale reading of 0.5 V and internal resistance of 10 MΩ.

Key features of the digital thermometerEstimate or measure the following for your digital thermometer:

SENSITIVITY (IN V OC-1 OR mV OC-1)

RESPONSE TIME

RESOLUTION (assuming voltmeter uncertainty is +/-0.01 V)

SYSTEMATIC ERROR (if present)

PRECISION

Strain gauges and response time

Explain the meaning of the term response time and explain its importance in the context of sensing.Explain how a resistive strain gauge works.

Simple sensing circuits

Many simple sensing circuits use a sensor in series with a resistor.

Response time

Length of time a sensor takes to reach its final reading following a sharp change in input.

Note:Needs to be short enough to detect any important changes. Changes more rapid than response time will be averaged out.

Sensitivity

Ratio of change of output to change of input.

Strain gauges

Strain gauges

Wheatstone bridge

Galvanometer measures when current is zero very accurately.If you know R1, R2, Rv and you know there is zero current, you can work out Ru very accurately.

e.g.: strain gauge