Unit 2.2 Electric Circuits

What are the types of semiconductor components (3)

1) Thermistor 2) LDRs 3) Diodes (and LEDs)

CORE PRACTICAL 7: Determine the *resistivity* of a material Procedure

*Assuming* the cross sectional *area of a wire is circular*,

What is power and it's 2 main equations

*Power* (P) is defined as the *rate of doing work*. It's measured in watts (W), where *1 watt* is equivalent to *1 joule of work done per second.* *P = VI or P = W/t* because V = W/t and I = Q/t so VI = WQ/tQ = W/t

What are the current, voltage and resistance rules for parallel circuits (3)

1) *current is split at each junction*, so: *I = I1 + I2 + I3* 2) *same p.d. across all components *(remember that within a loop the e.m.f. equals the sum of individual p.d.s) 3) R total = (R1 + R2 + R3)^-1

What are the current, voltage and resistance rules for series circuits (3)

1) *same current* at all points of the circuit (since there are no junctions) 2) *e.m.f. split between components* (by Kirchhoff's 2nd law), so: e = V1 + V2 + V3 3) *Rtotal = R1 + R2 + R3*

What is the I-V characteristic for a metallic conductor

1) At *constant temperature*, the *current* through a metallic conductor, e.g. a wire or a resistor, is *directly proportional to the p.d.*. 2) The fact that the characteristic *graph is a straight line through the origin* tells you that the *resistance doesn't change* — it's *equal to 1/gradient*. 3) The *SHALLOWER the gradient* of the characteristic I-V graph, the *GREATER the RESISTANCE*. 4) Metallic conductors are *ohmic* — they have *constant resistance* provided their *temperature doesn't change .*

How can you investigate the power output and efficiency of an electric motor (not a core practical)

1) Attach a *mass, m, to a motor*. Then close the switch. The motor will turn on, winding the string around the axle and raising the mass. 2) Record the *time taken, t, for the motor to raise the mass a set distance*, ∆h, e.g. 50 cm, using a *stopwatch* and the *metre ruler.* 3) Calculate the *work done against gravity* by the motor to raise the mass by: *∆E grav = mg∆h*. 4) You can then *calculate the power output of the motor*, using the equation *P = W/t* 5) You could also investigate the *efficiency* of the motor when lifting a given mass. You'd need to measure the *potential difference across the motor*, and the *current through it*, as it lifts the load. You could then calculate the *input power using P = VI.* You could then calculate the efficiency of the motor using the equation: Efficiency = (useful power output ÷ total power input)

Why do different materials (metals, semiconductors and insulators) have different resistivities (explained by I = nqvA)

1) In a *metal*, the *charge carriers* are *free electrons* — they're the ones from the *outer shell *of each atom. Thinking about the formula I = nqvA, there are *loads of charge carriers per unit volume*, making *n big*. The *drift velocity is small, even for a high current*. 2) *Semiconductors have fewer charge carriers*, so the *drift velocity needs to be higher* to give the *same current.* 3) A *perfect insulator* would have *no charge carriers*, so *n = 0* in the formula and you'd get *no current.* *Real insulators* have a *very small n.*

CORE PRACTICAL 8: Determine the e.m.f. and internal resistance of an electrical cell Procedure

1) Set up the apparatus on the right with an *ammeter, voltmeter, battery and variable resistor* 2) *Vary the current* in the circuit by *changing the* value of the *load resistance (R)* using the *variable resistor. *Measure the p.d*. (V) for several *different values of current* (I). 3) *Repeat several times* and find *average VT and I* 4) Record your *data for V and I in a table*, and *plot the results in a graph of V against I. (NOT IV)* 5) *Rearrange* the equation: e = V + Ir in the form V = -Ir + e (y = mx + c) 6) So the *intercept* of the straight line graph *= e* and the *gradient = -r*

How can a potential divider be used with an LDR or NTC thermistor to make a light or temperature sensor

1) The *resistance* of an *LDR or Thermistor* *changes* with a change in *light intensity or temperature* (inverse relation) 2) Either of these can be *used as one of the resistors* in a *potential divider*, giving an *output voltage* that *varies with the light level or temperature.* The diagram shows a *sensor* used to *detect light levels*. When *light shines on the LDR* its *resistance decreases*, so *Vout increases.*

What is the I-V characteristic for a filament lamp

1) The characteristic graph for a filament lamp is a *curve, which starts steep but gets shallower* as the *potential difference rises*. 2) The filament in a lamp is just a *coiled up length of metal wire,* so you might think it should have the same characteristic graph as a metallic conductor. However, *current flowing through the lamp* *increases its temperature*, so its *resistance increases*

PRACTICE CIRCUIT PROBLEMS

1) https://mathsmadeeasy.co.uk/wp-content/uploads/2017/10/AS-Physics-Electricity-Complete-Circuits-2-Answers-AQA-Edexcel-OCR.pdf 2) https://www.physicsandmathstutor.com/past-papers/a-level-physics/aqa-unit-1-by-topic/ 3) https://mathsmadeeasy.co.uk/wp-content/uploads/2017/10/AS-Physics-Electricity-Complete-Circuits-Questions-AQA-Edexcel.pdf

CORE PRACTICAL 7: Determine the *resistivity* of a material Procedure

Assuming the cross sectional area of a wire is

What is the I-V characteristic of a diode/LED

Diodes (including LEDs) are designed to let *current flow in one direction only*. You don't need to be able to explain how they work, just what they do.???????? 1) *Forward bias* is the *direction in which the current is allowed to flow* — it's the *direction the triangle points* in the *circuit symbols* of diodes. 2) Most diodes require a *threshold voltage of about 0.6 V* in the *forward direction* before they will conduct. 3) In *reverse bias*, the *resistance of the diode is very high* and the *current that flows is very tiny (leakage current)*. 4) In some cases, once the *reverse voltage is large enough, it can overcome the large energy barrier in the opposite direction (V = W/Q)*

Example: e.m.f *Three identical cells* each with an e.m.f. of 2.0 V and an internal resistance of 0.20 Ω are connected in *parallel*. A current of 0.90 A is flowing through the circuit. Calculate the total p.d. across the cells.

First calculate the *lost volts, v, for 1 cell* using *v = Ir.* Since the *current* flowing through the circuit is *split equally between each of the three cells (parallel)*, the current through *one cell is I/3*. So for 1 cell: *v = I/3 × r = 0.90/3 × 0.20* = 0.30 × 0.20 = *0.06 V* Then find the *terminal p.d. across 1 cell* using the equation: V = e - v = 2 - 0.06 = 1.94 So the *total p.d.* *across the cells combined* *= 1.9 V (to 2 s.f.)* *(voltage same in parallel)*

What is an electromotive force (e.m.f) and its equation (same as voltage)

The total amount of *work the battery does on each coulomb of charge* is called its *electromotive force or e.m.f.* (e). Be careful — e.m.f. *isn't actually a force*. It's measured in *volts* *W = eQ or e = W/Q*

How can you test the I-V (current - voltage) characteristics of a component (circuit setup and graph)

Using a test circuit: 1) Use the *variable resistor* to *alter the p.d.* across the component *and the current flowing* through it, and *record V and I using voltmeter and ammeter*. 2) *Repeat* your measurements and take *averages* to *reduce the effect of random errors* on your results. 3) *Plot a graph of current against p.d.* from your results. This graph is the I-V characteristic of the component.

How can you calculate total energy (W)

W = VIt (or W = V^2/Rt = W = I^2Rt)

How can a potentiometer be used in a stereo or bulb

You can use it to *change a voltage continuously*, like in the *volume control of a stereo:* You could also use this to *vary the brightness of a bulb* END: CHECK EXAM QUESTIONS IN CGP BOOK

Why can potential dividers be useful and what is a use for a voltmeter

You can use potential dividers to supply a potential difference, Vout, between zero and the potential difference across the voltage source. This can be useful, e.g. if you need a *specific varying p.d*. supply or one that is at a *lower p.d. than the voltage source.* - This circuit is mainly used for *calibrating voltmeters, *which have a very *high resistance.*

CORE PRACTICAL 7: Determine the *resistivity* of a material Safety (2)

• *Small voltage* so *little danger of electric shock* • *Wire may get warm* so *don't touch* unless with probe and *disconnect wire between readings*

CORE PRACTICAL 8: Determine the e.m.f. and internal resistance of an electrical cell Safety

• *low pd* so *no danger of shock*, • but *variable resistor may get hot*, so handle with care

CORE PRACTICAL 8: Determine the e.m.f. and internal resistance of an electrical cell Evaluation (4)

• For *small voltage/current values* use *new cell* or one with a *higher E.M.F.* • The *terminal PD* can be *measured across the terminals* of the power supply, *or across the component* • Keep *temperature constant* by *opening switch between readings* to *prevent current flow* in between each trial • Check for *zero errors on voltmeters and ammeters*

How do you calculate current with mean drift velocity

*I = nqvA* where: 1) I = current (A) 2) *n = number density of charge carriers (m-3)* (number *per unit volume*) 3) q = charge on each charge carrier (C) - the charge on each electron is -1.60 × 10^(-19) C 4) A = cross-sectional area (m2 )

Where does resistance come from

*Electrons colliding with atoms and losing energy.*

What is lost volts

*The energy wasted per coulomb overcoming the internal resistance.*

What is the formula to find the total e.m.f (by energy conservation)

*energy per coulomb* supplied by the *source (e)* = *energy per coulomb* used in *load resistance (R)* + *energy per coulomb* *wasted in internal resistance(r)* *e = IR + Ir* or *e = V + Ir* so *V = e - Ir* *Ir can also be written as v (lost volts) and IR as V (p.d.)*

CORE PRACTICAL 7: Determine the *resistivity* of a material Procedure

1) *Assuming* the cross sectional *area of a wire is circular*, use a *micrometer to measure the average diameter of 3 different points* then *divide by 2* to find *radius*. Use formula *πr^2 to find cross-sectional area* 2) *Clamp* the *test wire to the ruler* and *attach the crocodile clip* to the wire at the *'zero' end of the metre ruler* 3) *Attach the movable contact* to the *test wire*. *Record the length of the test wire connected* in the circuit, the *voltmeter and the ammeter reading*. 4) Use formula *R = V/I* to *find resistance*, then *repeat for different lengths* e.g. *at 10 cm intervals* 5) Plot a *graph of resistance against length*. The *gradient of the line of best fit* is *= R/I = ρ/A* . So *multiply the gradient* by the *cross-sectional area*to find the *resistivity of the wire* material. 6) The *resistivity* of a material *depends on temperature*, so keep the *temperature constant*. e.g. only having *small currents flow through the wire. (prevents overheating)*

Why does the resistivity of a metal increase as temperature increases

1) *Charge* is carried through metals by *free electrons* in a *lattice of positive ions*. 2) *Heating up a metal* makes *lattice of ions vibrates more* when heated, meaning the *electrons collide with them more frequently, transferring* some of their *kinetic energy* into other forms. 3) When *kinetic energy is lost* by electrons, their *speed and therefore mean drift velocity decreases*. 4) As *current is proportional to drift velocity, (I = nqvA)* this means the *current in the wire decreases* so its *resistance (and its resistivity*) *increases.*

What does the mean drift velocity current equation tell us (*I = nqvA*) (4 things)

1) *Double the number of charge carriers doubles the current* 2) If the *carriers move twice as fast* you get *twice the charge in the same time* — *twice the current.* 3) *Doubling the area also doubles the current.* 4) *Doubling the charge carried* by each carrier gives you *twice the charge in the same time* — *twice the current.*

What are the 3 things that determine resistance

1) Length (l). The *longer the wire* the *higher resistance* (harder for current to flow). 2) Area (A). The *wider the wire* the *less resistance*. 3) *Resistivity* (r). This depends on the *material* the wire's made from, as the structure of the material may make it *easy or difficult for charge to flow*. In general, resistivity depends on environmental factors as well, like *temperature.*

What is Kirchoff's 2 Laws *(conservation law)*?

1) The *total current entering a junction = the total current leaving* it. *Charge is conserved so current is also* because current is the rate of flow of charge 2) The *total e.m.f. around a series circuit* = the *sum of the p.d.s across each component*

What is a potential divider

A combination of *resistors in series* connected *across a voltage source (e.g. battery)* to produce a *required pd* - The *potential difference* across the voltage source (e.g. a battery) is *split in the ratio of the resistances* (current same series. Voltage split) e.g. So, if you had a 2 Ω resistor and a 3 Ω resistor, you'd get 2/5 of the p.d. across the 2 Ω resistor and 3/5 across the 3 Ω.

What direction do positive and negative charges flow

A flow of *positively-charged particles* produces exactly the *same current as an equal flow of negatively-charged particles* in the *opposite direction*. This is why we use *conventional current*, defined as *'in the same direction as a flow of positive charges'.*

What is a potentiometer

A potential divider that *replaces R1 and R2 with a variable resistor.*

Describe and explain the *I-V characteristic* of a thermistor

As the *voltage increases*, the *current increases*. More current leads to an *increase in temperature* and so a *decrease in resistance*. This in turn means *more current can flow*, so the *graph curves upwards* *Warming the thermistor* gives more *electrons enough energy to escape from their atoms*. This means that there are *more charge carriers available*, so the *current increases* and the *resistance decreases (R = V/I).*

Example: Voltage A kettle runs off the mains supply (230 V) and has an overall efficiency of 88%. Calculate how much electric charge will pass through the kettle if it transfers 308 J of energy to the water it contains.

Energy transferred to water = 0.88 × electrical energy input so the energy input will be *308 / 0.88 = 350 J* V = W/Q so Q = W/V Q = 350 ÷ 230 Q = 1.521... = 1.5 C (to 2 s.f.)

How can you work out the total e.m.f for multiple cells in series and parallel

For series: e total = e1 + e2 + e3 +... For parallel e total = e1 = e2 = e3 = ...

Example: I = nqvA Q3) Copper has 1.0 × 1029 free electrons per m3 . Calculate the mean drift velocity of the electrons in a copper wire of cross-sectional area 5.0 × 10-6 m2 when it is carrying a current of 13 A. (there is a charge of 1.60 × 10^(-19)C in an electron)

I = nqvA so v = I / nqA so v = 13 ÷ ((5.0 × 10-6) × (1.0 × 1029) × (1.60 × 10-19)) = 1.625 × 10-4 = 1.6 × 10-4 ms-1 (to 2 s.f.)

How can a variable resister vary the voltage of Vout in a potential divider

If you *replace R1 with a variable resistor*, you can *change Vout*. When R1 = 0, Vout = Vs . *As you *increase R1, Then it will have a high p.d.* (but *same current* - series) but *Vout gets smaller because there is less voltage left* and *current is still the same (series) so voltage decreases (V = IR)*.

How does a potentiometer work to vary voltage

Imagine you have a *long length of wire* connected to a power supply. If the *wire is uniform* (i.e. *same cross-sectional area and material*), then its *resistance is proportional to its length*. This means that if you were to *connect a voltmeter across different lengths of the wire*, the *pd* you'd record would be *proportional to the length* you'd *connected* it over You *move a slider* to *adjust the relative sizes of R1 and R2*. That way you can *vary Vout from 0 V up to the source voltage*

What are semiconductors

Materials that have *higher resistivity than conductors* but lower than insulators *(small number of charged particles)*

What is Ohm's Law?

Provided the *temperature is constant*, the *current through an ohmic conductor* is *directly proportional to the potential difference across* it (that's I ∝ V).

How do you calculate resistance given the length of the wire and area

R = ρl/A where ρ = *resistivity in Ωm A = cross-sectional area in *m2* l = length in *m* This means typical values for the *resistivity of conductors are really small.*

What is resistance and its formula

Resistance is potential voltage per unit voltage R = V / I Resistance is measured in Ohms (Ω)

what is internal resistance?

The *resistance inside the battery*/cell/power supply caused by the *electrons (moved by the chemical energy) colliding with atoms inside the device.* So *some energy is lost as heat*

How does temperature affect resistance in a Negative Temperature Coefficient (NTC) thermistor

The *resistance* of an (NTC) thermistor *decreases with increasing temperature.*

What is the resistivity of a material and what is it measured in (definition) *Resistivity is not = to resistance

The *resistivity* of a material is defined as the *resistance of a 1 m length with a 1 m2 cross-sectional area*, so ρ = RA/l . Resistivity is measured in *ohm metres (Ωm)*

What is current and its formula and how is it measured

The current in a wire is like water flowing in a pipe. The amount of water that flows depends on the flow rate and the time. It's the same with electricity — *current is the rate of flow of charge measured with an ammeter* *I = ∆Q /∆t* I is current in Amps ∆Q is charge in coulombs - 1 coulomb is the amount of *charge* that passes in *1 second* when the *current is 1 ampere.* ∆t is time in seconds

How does light intensity affect resistance in an LDR and why?

The greater the intensity of light shining on an LDR, the lower its resistance The explanation for this is similar to that for the thermistor. In this case, *light provides the energy* that *releases more electrons from valence shells*. This means *more charge carriers,* which means a *higher current and a lower resistance*

What is potential difference and why is it not equal to e.m.f

The potential difference across the load resistance (R) is the *work done when one coulomb of charge flows through the load resistance (total resistance of all components)* *= V = IR* If there was *no internal resistance*, the terminal *p.d. would be the same as the e.m.f.* However, in real power supplies, there's always some *energy lost overcoming the internal resistance.*

What does the resistivity of a material depend on and why do some materials e.g. metals have lower resistivities than semiconductors

The resistivity of a material is related to the *number density of charge carriers*, (and their *mean drift velocity*, which often *varies with temperature*). The *higher the number of charge carriers*, (and their *mean drift velocity*), the *higher the current* at a given p.d. (as I = nqvA), and so the *lower the resistance* and therefore the *lower the material's resistivity (ρ = RA/l)*. The *number density of charge carriers varies greatly between different materials*, which means there can be a huge *variation in their resistivities*

What is voltage/potential difference and its equation and how is p.d. measured

Voltage is *work done per unit charge* The potential difference across a component is *1 volt (V)* when you do *1 joule of work moving 1 coulomb* of charge through the component. This defines the volt V = W/Q W is measured in Joules p.d. is measured in volts using a voltmeter in parallel

Example: Energy A current of 4.0 A flows through a kettle's heating element once it is connected to the mains (230 V). The kettle takes 4.5 minutes to boil the water it contains. How much energy does the kettle's heating element transfer to the water in the time it takes to boil?

W = IVt W = 4 x 230 x 4.5(60) W = 248,400 J = 250,000 J (2 s.f.)

What is the mean drift velocity

When *current flows through a wire*, you might imagine the *electrons* all moving uniformly in the same direction. In fact, they move randomly in all directions, but *tend to drift one way*. The *mean drift velocity is just the average velocity* and it's much, *much less than the electrons' actual speed. *(Their actual speed is about 1,000,000 ms-1.)

What are conduction holes in semiconductors

When an electron gains enough energy to enter the conduction band, it leaves behind a (positive) conduction hole. This *hole attracts another electron from another atom* which creates a *new conduction hole* The *positive hole starts to move towards the negative terminal* while *electrons move towards the positive terminal. at the same time* This *adds to the charge* in the circuit which *adds current*

How can you derive 2 more power equations from P = IV, P = W/t and R = V/I

You also know (from the definition of resistance) that *V = IR*. *Combining this with the equations P = IV and P = W/Q* gives you loads of different ways to calculate power: P = IV and P = W/t *P = V^2/R P = I^2R*

Example: Power A robotic mutant Santa from the future converts 750 J of electrical energy into heat every second. a) What is the operating power of the robotic mutant Santa? b) All of the robotic mutant Santa's components are connected in series, with a total resistance of 30 Ω. What current flows through his wire veins?

a) P = W/t P = 750/1 = 750 W b) P = 750 W, R = 30 Ω, I = ? Use equation: P = I^2R I^2 = P/R I^2 = 750/30 *I = 5.0 A*

Example: resistivity Q1 Aluminium has a resistivity of 2.8 × 10-8 Ω m at 20 °C. Calculate the resistance of a pure aluminium wire of length 4.0 m and diameter 1.0 mm, at 20 °C.

d = 1 mm = 1/1000 m so r = 1/2000 m A = π(1/2000)^2 = 7.85 x 10^-7 m^2 R = ρl/A R = 2.8 x 10^-8 x 4 / 7.85 x 10^-7 R = 0.1426 = 0.14 Ω (to 2 s.f.)

What happens when energy is supplied to semiconductors

if *energy is supplied* to some types of *semiconductor* (e.g. by *increasing their temperature*), *more charge carriers are released (electrons escape outer shells to the conduction bands)*, so the *current increases* (as I = nqvA) and their *resistance and resistivity decrease.*

What is superconductivity

when the *resistance* of some materials becomes *zero* below a * very, very low critical temperature* so *currents can be very high*

CORE PRACTICAL 7: Determine the *resistivity* of a material Evaluation

• *Highly varying voltage/current readings*: remove power supply, voltmeter, ammeter and *replace with ohm-meter* • *Uncertainty from micrometer* is *doubled as radius gets squared* • *Crocodile clip is not directly in contact* with the *exact end* of the wire due to windings on the end of the ruler • *Poor connection* between crocodile *clips and wire*/ dirty *crocodile clips creates will mean a higher resistance* is measured • Constant does not change resistivity at high temps - this is not a source of error • Use *ohm-meter to achieve resistance directly*, *reduce the wire heating* (uses a very *low current*) • Ensure *wire straight* so *length measurement accurate*