Electric Circuits Spec Points Flashcards
Ohms law when temperature is constant
The current flowing through a conductor is directly proportional to the potential difference across its ends.
Kirchoff’s first law - the electric current rule
The algebraic sum of the current entering and leaving a junction is equal to zero
This is a consequence of conservation of charge - current shouldn’t decrease or increase in a circuit when it splits
Conservation of charge
Charge cannot be created or destroyed, so in a closed loop, the flow of charge must be the same throughout
Kirchoff’s second law
The sum of all the voltages in a series circuit is equal to the battery voltage or the sum of all the voltages in a loop is zero.
Potential differences in circuits due to energy conservation
Series - battery p.d. Is shared across all elements in the circuit, therefore the total sum of the voltages across all elements is equal to the supply p.d.
Parallel - the p.d. Across each branch is the same
Deriving resistance in parallel
Electrical current rule
I = I1 + I2
Electrical voltage rule
V = V1 = V2
Rearranging ohms law for current (I=V/R)
V/R = V/R1 + V/R2
Since p.d. Is the same for all resistors, divide by V
1/R = 1/R1 + 1/R2
Deriving resistance in a series circuit
V = V1 + V2
Ohms law V=IR
IR = IR1 + IR2
Divide by I because it is the same for all resistors
R = R1 + R2
Diode I-V graph
- when the current is in the direction of the arrowhead symbol, this is forward bias.
This is shown by the sharp increase in p.d. And the current on the right side of the graph - when the diode is switched around, it does not conduct and is called reverse bias. This is shown by a zero reading of current or p.d. On the left side of the graph
- the threshold voltage at which a diode starts to conduct is typically 0.6V
Filament lamp I-V graph
Shows the current increasing at a proportionally slower rate than the potential difference
- because: as current increases, temp of the filament in the lamp increases
- since the filament is a metal, the higher temp causes an increase in resistance
- resistance opposes the current, causing the current to increase at a slower rate.
-where the graph is a straight line, the resistance is constant
- the resistance increases as the graph curves
- the filament lamp obeys ohm’s law for small voltages
Thermistor I-V grpah
Shallow curve upwards
- increase in pd results in an increase in current causing temp of thermistor to rise
- as temp rises, resistance decreases
- this means more current is able to flow through
Core practical 2: investigating resistivity
Aim + variables
Aim - to determine the resistivity of a length of wire
Independent - length of wire (m)
Dependent - the current through the wire (A)
Control - voltage across the wire
- material the wire is made from
Core practical 2: investigating resistivity
Equipment list
Ammeter
Voltmeter
2.0m of wire
Flying lead ( a wire with a crocodile clip at one end to allow connection at any point along the test wire)
Metre ruler
Micrometer
Power supply
Core practical 2: investigating resistivity
Resolution of measuring equipment
Metre ruler - 1mm
Micrometer - 0.01 mm
Voltmeter - 0.1V
Ammeter - 0.01A
Core practical 2: investigating resistivity
Method
- measure the diameter of wire using a micrometer
- measurement should be taken between 5-10 times randomly along the wire
- calculate mean diameter from these results
Set up equipment so the wire is taped or clamped to the ruler with one end of the circuit attached to the wire where the ruler reads 0. - the ammeter is connected in series and the voltmeter in parallel with the wire.
- attach the flying lead to the test wire at 0.25m and set the power supply at a voltage of 6.0V
- check that this is the voltage across the wire on the voltmeter
- read and record the current from the ammeter then switch off the current immediately after the reading
- this is to prevent the wire from heating up and changing the resistivity.
- vary the distance between the fixed end of the wire and the flying lead in 0.25m intervals until the full length
- record the current for each length at least three times and calculate an average current, I
- for each length calculate the average resistance of the length of the wire using the equation r=v/I
- R - average resistance of the length of the wire
- V - potential difference across the circuit
- I - the average current through the wire for the chosen length
Core practical 2: investigating resistivity
Analysis of resuslts
Resistivity = RA/l
Rearrange
R = pL/A
Y = mx
Y = R
X = L
M = p/A
Therefore to find resistivity:
- plot a graph of the length of the wire against the average resistance of the wire
- draw a line of best fit
- calculate the gradient
- multiply the gradient by cross-sectional area
A = pid^2/4
Core practical 2: investigating resistivity
Systematic errors
- the end of the wire that is attached to the circuit must start at 0 on the ruler
Otherwise this could cause a zero error in your measurements of the length
Core practical 2: investigating resistivity
Random errors
- only allow small currents to flow through wire
- the resistivity of a material depends on its temperature
-the current flowing through the wire will cause its temperature to increase - therefore the temperature is kept constant by small currents
- the current should be switched off in between readings so that there isnt a temperature rise
- calculate an average diameter
- this will reduce random errors in the reading
- make at least 5-10 measurements of the diameter of the wire with the micrometer
Core practical 2: investigating resistivity
Safety considerations
- when there is a high current, and a thin wire, the wire will become very hot
- do not touch the wire directly when the circuit is switched on
- switch off the power supply between readings and immediately if you smell burning
- keep liquids away from electrical equipment.
Why does the potential along a uniform current-carrying wire vary with the distance along it
Resistance of an object is dependent on its length
A uniform current-carrying wire has a constant resistivity and cross-sectional area.
When length increases, the resistance will increase uniformly. Using ohm’s law, potential will also increase
Principles of a potential divider circuit
A circuit with several resistors in series connected across a voltage source, used to produce a required fraction of the source potential difference, which remains constant.
You can also make the pd supply a variable pd by using a variable resistors as one
Potential divider equation
Vout = Vin (R2/R1+R2)
A LDR’s resistance decreases as light intensity increases
LDR = R1
Resistor = R2
What will V out do when light intensity falls
Resistance across R1 will increase
Total circuit resistance increases
Circuit current will decrease
Using Ohm’s law, voltage across R2 will decrease
So V out decreases
Define electromotive force
Energy transferred by a cell per coulomb of charge
What is internal resistance
Resistance within a battery that causes a drop in the source voltage when there is a current
Caused by electrons colliding with atoms inside the battery, therefore some energy is lost before electrons leave battery
Represented as a small resistor inside the battery
What is terminal potential difference
P.d. Across resistance R (load resistance)
When can the emf be measured using a voltmeter
Voltage across a cell when there is no current running through the cell which means it is an open circuit
Core practical 3: determine the emf and internal resistance of an electrical cell
Variables
Independent - resistance
Dependant - voltage and current
Control - emf of cell , internal resistance of cell
Core practical 3: determine the emf and internal resistance of an electrical cell
Equipment list + resolutions
1.5 V cell
Resistor - unknown resistance to act as internal resistance
100 ohm variable resistor
Voltmeter 1mV
Ammeter 0.1mA
Wires
Switch
Core practical 3: determine the emf and internal resistance of an electrical cell
Method
- Cell and resistor (r) shld be connected in series, considered to be a single cell
- Record V when switch is open
- Set variable resistor to its max value, close switch and record V and I
- Vary resistance up to a minimum of 8-10 readings
Ensure you take readings for the whole range of the variable resistor
Core practical 3: determine the emf and internal resistance of an electrical cell
Analysing results
E=I(R+r)
Rearrange to
V = -rI + E
Y = mx + c
Plot a graph of V against I and draw line of best fit
Measure gradient - negative internal resistance
Y intercept - emf
Core practical 3: determine the emf and internal resistance of an electrical cell
Evaluating - errors
Systematic
Only close the switch for as long as it takes to take each pair of readings. This will prevent internal resistance of the battery changing during the experiment
Random
Only use fairly new cells. Run down batteries can vary their internal resistance during an experiment
Wait for reading on ammeter and voltmeter to stabilise before reading results
Take multiple readings to reduce random errors
Core practical 3: determine the emf and internal resistance of an electrical cell
Safety considerations
- electrical components can get hot when used for a long period of time
- switch off power supply right away if there is a burning smell
- make sure there are no liquids close to the equipment
How can changes in resistance with temperature be modelled in terms of lattice vibrations and number of conduction electrons
As the temperature increases, the intensity of the vibration of its atoms also increases
The more intense the lattice vibrations are, the more difficult it is for free electrons to pass through it
This is because the electrons will be more likely to collide with the vibrating atoms if they are oscillating more intensely, causing them to slow down.
This increases the resistance
Apply to metallic conductors:
Changes of resistance with temperature modelled in terms of lattice vibrations
As temperature of a metal conductor increases, its atoms gain energy and once they gain enough energy, they begin to release electrons (thermionic emission). This increases the number of charge carriers available in the conductor, which decreases its resistance
Apply to NTC thermistors:
Changes of resistance with temperature modelled in terms of lattice vibrations
When their temperature increases, resistance decreases
Because they release a large amount of electrons as their temperature increases which frees up charge carriers (outweighing the effects of lattice vibrations)
How can resistance changes with illumination be modelled in terms of the number of conduction electrons
When light above a certain frequency is shone onto a metal, it releases electrons, which are known as photoelectrons. This is called the photoelectric effect
Apply to LDR:
Changes of resistance with illumination, modelled in terms of number of conduction electrons
LDRs are made from photoconductive materials, meaning that they release electrons in the presence of light. Therefore, as light intensity increases, electrons are released, which increases the number of charge carries available to conduct electricity, and the resistance of the LDR decreases
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