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Electricity

Simple Circuits

- A complete circuit is needed for a current to flow.
- A current is a flow of electrons which move from the –ve terminal of the power supply to the +ve. In Physics, however, we still show the current flow from +ve to –ve.
- The electrons are called charge carriers.

Metals contain at least 1 free electron per atom. The e’s move at random when no current flows leaving behind a positive ion.

- When a power supply is connected to a metal wire the e’s are attracted to the +ve terminal. They collide with the +ve ions which slows them down. The wire therefore has a certain amount of resistance.
- The e’s gain energy from the power supply and give it to the ions when they collide. This is why a metal gets hotter whenever a current flows.

- Charge can be carried by other charge carriers like ions and not just electrons. e.g.salty water will conduct a small current
- Insulators do not have any free electrons i.e. no conduction.

Charge and Current not just electrons. e.g.salty water will conduct a small current

- Current is the rate of flow of charge. For a current, I, the charge flow, ΔQ, for a time, Δt, isgiven by:
- I = ΔQ
Δ t

- OR ΔQ = IΔt
- e.g. QHow much charge flows when there is a current of 2A for 10 minutes
- AΔQ = I Δt
- =2A x 10 x 60
- = 1200C (coulombs)

- The charge on 1 electron is -1.6x10 not just electrons. e.g.salty water will conduct a small current-19C so we can find the number of e’s flowing by dividing the charge in C by the charge on 1 electron.
- e.g. -1200C
-1.6 x 10-19C

- = 7.50 x 1021 electrons

Electrical power and Energy not just electrons. e.g.salty water will conduct a small current

- The power supply does work in pushing the electrons around the circuit.
- The voltage across the power supply is called the e.m.f. (electromotive force).
- Whenever work is done there is a transfer of energy and the power supply gives energy to the circuit.

Definition of voltage or potential difference: not just electrons. e.g.salty water will conduct a small current

- The p.d. between 2 points is the work done per coulomb of charge moving between the 2 points.
- P.d = workor V = W
- charge Q
- Or 1V = 1JC-1
- Similarly, if the e.m.f. is 1.5V, then the power supply gives 1.5J of energy to each coulomb of charge.

- Re-arranging the equation V = not just electrons. e.g.salty water will conduct a small currentW
Q

- gives W = QVor W = ItV
- Remember W = work done = energy transferred
- Power is the rate of doing work or the rate of transfer of energy.
- P =W = E
t t

- Substituting for W gives
P = ItV =IV

t

- Power is measured in watts (W)

Resistance not just electrons. e.g.salty water will conduct a small current

- Resistance is the opposition to current flow. It is caused by collisions between the electrons and positive ions.
- Resistance = p.d. across component
- current through component
- R = V or V = IR
I

- Resistance is measured
in ohms (Ω)

Digital Multimeter not just electrons. e.g.salty water will conduct a small current

Measuring current not just electrons. e.g.salty water will conduct a small current

- We measure current using an ammeter placed in seriesin the circuit.
- A perfect ammeter would have zero resistance so that it does not alter the size of the current that it is measuring.
- All connecting leads should also have zero resistance.

Measuring p.d. not just electrons. e.g.salty water will conduct a small current

- A voltmeter is used to measure the voltage or potential difference(p.d.) across a component.
- A voltmeter is always connected in parallel with the component.
- A voltmeter should have a very highresistance so that it does not take any current from the circuit.

Measuring resistance not just electrons. e.g.salty water will conduct a small current

- Connect up the circuit shown in fig.1 on P51
- Use the variable resistor to obtain 7 pairs of readings of current and p.d.
- Plot a graph of p.d. against current
- Sine V = IR the gradient of this graph gives the resistance.
- Resistance can also be measured directly with an ohm-meter.

Resistivity not just electrons. e.g.salty water will conduct a small current

- Long wires have more resistance than short wires
- Thin wires have more resistance than thick wires.
- Different types of wire have different resistance.
- We can calculate the resistance of a wire using
Resistance = resistivity x length

X- sectional area

R = ρl

A

- Definition: ρ = RA = resistance x area
- l length
- Resistivity is a property of the material whereas resistance is a property of the component.

See the table on P.52 for the resistivities of various materials.

- Metals have a low resistivity and insulators have a high resistivity. Semi-conductors are somewhere in the middle.
- The units for resistivity are Ωm.

Example materials.

- Find the resistance of a 50cm length of copper wire with a cross sectional area of 1 x 10-6m2
- R = ρl
- A
- = 1.7 x 10-8 x 0.5
- 1 x 10-6
- = 8.5 x 10-3Ω

Superconductivity materials.

- Some materials lose all their resistance below a certain critical temperature. e.g. mercury has no resistance below -269°C.
- Superconducting wires do not become hot, because electrons can flow through them without any transfer of energy. This is useful for power lines.
- Very strong electromagnets can also be made using superconductors.

Controlling Voltage and current materials.

- A rheostat or variable resistor in series with a component can control the current through it.
- A rheostat has a maximum resistance so it cannot reduce the current to zero.

Potential Divider materials.

- A rheostat can be used as a potential divider.
- As the sliding contact moves from one end to the other, the output increases from 0 –max. i.e. any fraction of the whole voltage can be obtained.

Supplying a variable voltage materials.

- We now have 3 methods for supplying a variable voltage:
- A variable resistor in series with the power supply
- A variable power supply. (e.g our black supplies but they will only supply a small current).
- A fixed power supply with a rheostat connected to it as in the potential divider circuit.

I-V materials.Graphs

- Set up the circuit shown in fig.2(a) on P 53 and use the potential divider circuit to obtain 7 pairs of values of current and p.d. for a resistor, lamp and diode for both positive and negative values of p.d.
- Plot a graph of current against p.d. fpr each one.
- You can aslo do this using sensors.

Graphs materials.

I materials. – V Graphs

- For a fixed resistor the graph is a straight line through the origin.
- Current is directly proportional to voltage
- This is called Ohm’s law and applies to many resistors and metals at constant temperature. Such components are described as ohmic conductors.

- For a materials.lamp the graph is not a straight line through the origin so Ohms law is not obeyed.
- Lamps get hotter as the current increases. This causes an increase in its resistance and the I-V graph becomes less steep. i.e. as the p.d increases the current increases by smaller amounts

- The materials.diode allows current to flow in one direction only. This is called the forward direction. The current increases dramatically once a certain voltage has been reached.
- Very little current flows in the reverse direction. It has a very high resistance in this direction.

Change of Resistance materials.

- The resistance of a metal increases with temperature. It has a positive temperature coefficient
- A rise in temperature causes an increase in the vibrations of the +ve ions so the e’s collide more frequently.

Thermistors materials.

- As the temperature increases the resistance of the thermistor decreases andthe current therefore increases
- A thermistor can be used to make a thermometer by calibrating a milliammeter in ºC instead of mA when connected in series with the thermistor

- Since the resistance of a thermistor materials.decreases as the temperature increases we say it has a negative temperature coefficient
- Semi-conductors have covalent bonds joining atoms together. As the temperature rises more e’s are released as these bonds break. Since there are more charge carriers, the current increases.
- Thermistors are therefore used in temperature sensitive devices.

Current in series circuits materials.

- In a series circuit:
- The current is the same size all the way round the circuit.
- The size of the current depends upon the supply voltage and the amount of resistance in the circuit

Currents in Parallel circuits materials.

- The sum of the currents entering any point in a circuit is equal to the sum of the currents leaving that point. (This is called
Kirchhoff’s 1st Law)

- The current through each branch of a parallel circuit depends on the resistance of that branch and is independent of the other branches.

Potential Difference in Series Circuits materials.

The e.m.f of the battery in a series circuit is equal to the sum of the potential differences across the components

V1 = V2 + V3

Parallel circuits materials.

The voltage (potential difference) across each branch in a parallel circuit is equal to the e.m.f. of the battery.

V1 = V2 =V3

Think! materials.

- Two different light bulbs are connected in series to the same power supply. Explain why one glows brighter than the other

Resistors in series and in parallel materials.

- See P.61-62 for proofs of these formulae that you are given.
- For resistors in series, Rt = R1+ R2
- For resistors in parallel,
- If there are n resistors in parallel and they each have resistance R then Rt = R
n

Calculating Power from Resistance materials.

- When current flows through
a resistor, work is done on

the resistor and it gets hot.

e.g. in an electric iron

- The rate of doing work or power is given by P=IV = I(IR)
- i.e. P = I2R (GIVEN)
- This gives the rate at which heat energy is transferred to the surroundings.

EMF and Internal Resistance materials.

- Connect a voltmeter across
the terminals of a cell and

record the reading.

- This is called the terminal p.d.
- This is also the e.m.f of the cell. The e.m.f. gives the total work done per coulomb of charge that flows around the circuit.
ε= Wt

Q

- Now connect up to 3 lamps in parallel and note the reading on the voltmeter.
- The terminal p.d. falls as current is drawn from the cell. The difference between the e.m.f. and the terminal p.d. is called the lost volts.
- This is because some p.d. is being used to drive the current through the cell itself. The cell has internal resistance.
- Definition: Internal resistance is the resistance to flow of current inside the cell itself.

- The emf of a cell in any series circuit = sum of the p.d.’s around the circuit
- i.e. emf of cell = terminal p.d. + “lost volts”
- ε = V + v
- If a cell of emf, ε, with
internal resistance, r,

is connected to an

external resistor, R, then:

- ε = IR + Ir
- This can also be written as ε = V +Ir
- OR ε = I(R + r)

- Rearranging gives p.d.’s around the circuitV = ε– Ir (Given)
- We can rewrite this as V = -Ir + ε
V = -rI + ε

- The equation of a straight line is y= mx + c
- so if we plot a graph of V against I then:
- The line is a straight line with a negative gradient.
- The gradient = internal resistance
- The intercept give the e.m.f of the cell. i.e the emf = p.d at zero current

Electrical Power p.d.’s around the circuit

- Since ε = IR + Ir
- We can multiply by I to give:
- Iε = I 2R + I 2r
- i.e. power supplied by cell = power delivered to the external resistor, R + power wasted in cell due to its internal resistance
- The graph on P 65 shows that the power delivered to a resistor, R (the load) is a maximum when R = r

Effects of Internal Resistance p.d.’s around the circuit

- When a cell is short circuited r is the only resistance.
- For a 1.5V dry cell r = 0.5Ω and I = 3A
- Rechargeable cells have a very low internal resistance so I can be dangerously large.
- In any circuit if R = 0, then I = ε and r
r

limitsthe size of the current

Car batteries and E.H.T.Power supplies p.d.’s around the circuit

- Car batteries and low voltage power supplies have a very low internal resistance so they can provide a large current.
- An E.H.T. power supply has a very large internal resistance to limit the current it supplies to a safe value.

Cells in series p.d.’s around the circuit

- When cells are connected in series the total emf = sum of emf’s and the total resistance = sum of internal resistances
- e.g. 4 cells of emf, 1.5V and internal resistance, 1Ω have a total emf of 6V and total internal resistance of 4Ω

Cells in parallel p.d.’s around the circuit

- When cells are connected in parallel the emf is the same as for one cell i.e ε
- If the internal resistance of each cell is r, then they must be combined together in parallel so if there are n cells then the total internal resistance = r
n

- e.g If there are 4 cells of emf 1.5V and internal resistance, 4Ω then the total emf = 1.5V and the internal resistance = 1Ω

The Potential divider p.d.’s around the circuit

- Using a chain of resistors as shown in fig 1 on P70 we can see how the p.d. from a source can be divided in proportion to the resistances.
- We have already seen when plotting the
I-V graphs how a variable resistor can be used to give any fraction of the maximum p.d from a power supply.

Other uses of a potential divider p.d.’s around the circuit

- As an audio “volume control”. The cell in the potential divider circuit is replaved with the audio signal p.d. The variable output is then supplied to a loudspeaker.
- In a dimmer switch to vary the brightness of a lamp from zero to a maximum

Light sensitive potential divider p.d.’s around the circuit

- Set up the circuit shown in fig 4 on P71.
- As the light intensity increases the resistance of the LDR decreases and the voltage across it decreases. The output decreases.
- If the variable resistor and LDR are then swapped the output p.d. increases as the light intensity increases and the circuit can be used as a light meter.

Temperature Sensitive p.d.’s around the circuit Potential Divider

- Set up the circuit shown in fig 4 on P71.
- As the temperature increases the resistance of the thermistor decreases and the p.d decreases.
- If the varaiable resistor and thermistor are swapped round the output p.d. increases as the temperature rises. The circuit could be used to operate an alarm if the temperature becomes too high.

Alternating currents p.d.’s around the circuit

- Direct current from a battery moves in one direction only, from positive to negative.
- In alternating current the direction is changing all the time. The charge carriers are moving forwards and backwards many times a second. In Europe it is 50 Hz (cycles per second)
- AC and DC are equally good at heating, lighting, or running motors.

- This graph shows the difference between d.c. and a.c. p.d.’s around the circuit

- One complete alternation is called a p.d.’s around the circuitcycle.
- The frequency is the number of cycles per second. Units are hertz (Hz).
- The period is the time taken for one cycle. It is measured in seconds. f = 1/T.
- The current follows exactly the same wave form as voltage.
- The graph is called a sinusoidalwaveform or a sine wave.

Peak values p.d.’s around the circuit

- The peak value of current or p.d. is the maximum value of current or p.d.
- The peak value can be found from the amplitude of the wave.
- The peak-to-peak value = 2 x peak value
- e.g. If the peak value is 300V then the peak-to-peak value is 600V

Root-mean square (r.m.s.) values p.d.’s around the circuit

- This is the value of direct current which has the same heating effect as the alternating current in the same resistor.

Calculating rms values p.d.’s around the circuit

- The proof on P76 shows that the rms values of current or p.d. = 1 x peak value
√2

- If the peak current = Ioand the peak p.d. =V0
- then

Example p.d.’s around the circuit

- Q The rms value of the mains in the UK is 230V. Calculate the peak value and the peak-to-peak value
- A Vo = √2 x Vrms
- = √2 x 230
- = 325V
- Peak-to-peak = 650V

Calculating Power p.d.’s around the circuit

- For dc, power = current x voltage
- For ac, the peak power = I0x Vo
- The power varies between I0Vo and zero
- Average power = I0x Vo = I0x Vo = Irms x Vrms
- 2 √2 √2

Oscilloscopes p.d.’s around the circuit

Oscilloscopes p.d.’s around the circuit

- Inside the oscilloscope there is a beam of electrons which hit the screen to produce a dot.
- This dot can be made to move across the screen at different speeds by adjusting the time base.
- If it is moving fast enough a straight line is produced.
- The dot/line can also be made to move up/down by connecting a signal to the y-input.

Uses p.d.’s around the circuit

- An oscilloscope is connected in exactly the same way as a voltmeter, i.e. in parallelwith a component. (The input resistance is very high)
- An oscilloscope can be used as a DCvoltmeter. We get a horizontal line or a dot, depending whether the time base is on. If it is used as an AC voltmeter, it will show the sinusoidal waveform

Controls p.d.’s around the circuit

- The most important controls that we use are:
- The y-gain setting, calibrated in Vcm-1.
- The time base, in scm-1.
- We measure the voltage on the vertical axis. We can adjust the sensitivity by turning the knob marked y-gain.
- The horizontal direction is determined by the time basesetting. We can change this by using the time base knob.

Example using ac p.d.’s around the circuit

- Q p.d.’s around the circuitThe time base is set at
- 2 mscm-1 and the
- y gain at 0.5 Vcm-1
- (a) What is the peak to peak voltage?
- (b) What is the peak voltage?
- (c) What is the rms voltage?
- (d) What is the period?
- (e) What is the frequency?

Answers p.d.’s around the circuit

- (a) The total height of the wave from peak to trough is 6.4 cm So Vpk-to-pk = 3.2 V
- (b) Vpk = 3.2/2 = 1.6 V
- (c) Vrms = Vpk /2 = 1.6 /2 = 1.13 V
- (d) 1 cycle is 2.9 cm
- Time period = 2.9 2 = 5.8 ms = 5.8 10-3 s (e) f = 1/T = 1/5.8 10-3 = 178 Hz

Examples using dc p.d.’s around the circuit

- 1. using a d.c source with the time base on
___________

- __________
- p.d. = 0 p.d. = 0.5V
- Using y-gain setting the input voltage can be found.

3. Pulse followed by echo p.d.’s around the circuit

- The time between a pulse of current and its echo can be found directly using the time base setting. See fig4 on P78

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