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Current-Voltage Characteristics
Basics of Electricity
Electric Current Electric current is defined as o The rate of flow of electric charge Current flows when a circuit is formed o This is when a conductor, such as a wire, connects two oppositely charged terminals of a source, such as a cell In electric circuits, the current is a flow of electrons Conventional current is defined as the flow of positive charge o This is from the positive terminal of a cell to the negative terminal This is the opposite of the direction of electron flow o Electrons are negatively charged so they flow from the negative terminal of a cell to the positive terminal Ammeters must be connected in series with the component being measured Potential Difference Potential difference is defined as o The electrical work done per unit charge flowing between two points
A simple cell creates a potential difference through the separation of charge o One end ( terminal ) of the cell has an excess of positive charge and the other an excess of negative charge o Negatively charged electrons are repelled by the negative terminal and attracted to the positive terminal o Therefore, when a wire is connected between the two terminals, the potential difference causes the flow of electrons ( current )
Current-Voltage Characteristics
Ohm's Law Ohm’s law states: o For a conductor at a constant temperature, the current through it is proportional to the potential difference across it Constant temperature implies constant resistance
Since the gradient is constant, the resistance R of the resistor can
be calculated by using 1 ÷ gradient of the graph An electrical component obeys Ohm’s law if its graph of current against potential difference is a straight line through the origin o A resistor does obey Ohm’s law o A filament lamp does not obey Ohm’s law This applies to any metal wires, provided that the current isn’t large enough to increase their temperature
I–V Characteristics
This is because: o As the current increases, the temperature of the filament in the lamp increases o Since the filament is a metal, the higher temperature causes an increase in resistance o 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
Resistance & Resistivity
Resistivity
As free electrons move through a metal wire, they collide with ions which get in their way As a result, they transfer some, or all, of their kinetic energy on collision , which causes electrical heating Since current is the flow of charge , the ions resisting their flow causes resistance Resistance depends on the length of the wire, the cross-sectional area through which the current is passing and the resistivity of the material The resistivity equation shows that: o The longer the wire, the greater its resistance o The thicker the wire, the smaller its resistance Resistivity is a property that describes the extent to which a material opposes the flow of electric current through it It is a property of the material, and is dependent on temperature
The higher the resistivity of a material, the higher its resistance
Resistance in a Thermistor
Electric current is the flow of free electrons in a material o The electrons collide with the vibrating atoms which impede their flow, hence the current decreases So, if the current decreases, then the resistance will increase
(from V = IR)
Therefore, for a metallic conductor which obeys Ohm's law: o An increase in temperature causes an increase in resistance o A decrease in temperature causes a decrease in resistance This is not the case for components such as a thermistor o For a thermistor, an increase in temperature causes a decrease in resistance A thermistor is a non-ohmic conductor and sensory resistor whose resistance varies with temperature Most thermistors are negative temperature coefficient (ntc) components. o This means that if the temperature increases, the resistance of the thermistor decreases (and vice versa) Thermistors are temperature sensors and are used in circuits in ovens, fire alarms and digital thermometers o As the thermistor gets hotter , its resistance decreases o As the thermistor gets cooler , its resistance increases
In a series circuit, the current is the same for all components In a parallel circuit, the current is split across the different branches (or junction). The total current into a junction must equal the total current out of a junction o The amount of current in each branch depends on the total resistance of the components within that branch Potential Difference In a series circuit, the e.m.f of the power supply is shared amongst all the components in different amounts, depending on their resistance In a parallel circuit, the voltage of all the components in each branch is equal to the e.m.f of the power supply Cells can also be connected in series or parallel The total voltage of the combined cells can be calculated in the same way as voltage o If the cells are connected in series , the total voltage between the ends of the chain of cells is the sum of the potential difference across each cell o If the cells are connected in parallel , the total voltage across the arrangement is the same as for one cell Conservation of Charge Charge is never used up or lost in a circuit - this is known as conservation of charge As a result of this, for current in a parallel circuit: o The sum of the currents entering a junction always equal the sum of the currents out of the junction This is sometimes known as Kirchhoff's First Law In a circuit: o A junction is a point where at least three circuit paths meet
o A branch is a path connecting two junctions If a circuit splits into two branches, then the current before the circuit splits should be equal to the current after it has split Conservation of Energy Energy is never used up or lost in a circuit - this is known as conservation of energy As a result of this, for voltage in any circuit: The total e.m.f. in a closed circuit equals the sum of the potential differences across each component This is sometimes known as Kirchhoff's Second Law Each closed circuit can be treated like a series circuit Below is a circuit explaining Kirchhoff’s Second Law with the sum of the voltages in the closed series circuit equal to the total e.m.f:
Electrical Energy & Power
In mechanics, power P is defined as the rate of doing work
o The potential difference is the work done per unit charge o Current is the rate of flow of charge Therefore, the electrical power is defined as the rate of change of work done : o P = E / t = W / t o P = Power (W) o E = energy (J) o t = time (s) o W = work done (J)
Potential Divider Circuits
Potential Divider Circuit When two resistors are connected in series, through Kirchhoff’s Second Law, the potential difference across the power source is divided between them Potential dividers are circuits which produce an output voltage as a fraction of its input voltage Potential dividers have three main purposes: o To provide a variable potential difference o To enable a specific potential difference to be chosen o To split the potential difference of a power source between two or more components Potential divider circuits are based on the ratio of voltage between components. This is equal to the ratio of the resistances of the resistors in the diagram below, giving the following equation: o Vout = (R 2 / R 1 + R 2 ) Vin Where:
o R 2 is the numerator and the resistance of the resistor
over Vout
o R 1 is the other resistance in series
o Vout is the output potential difference
o Vin is the input potential difference
The potential divider equation can also be written: Vout = (R 1 / R 1 + R 2 ) Vin Where this time:
o R 1 is the numerator and the resistance of the resistor
over Vout
o R 2 is the other resistance in series
Electromotive Force & Internal Resistance
Electromotive Force & Internal Resistance
Electromotive Force When charge passes through a power supply such as a battery, it gains electrical energy Electromotive force (e.m.f) is defined as: The amount of chemical energy converted to electrical energy per coulomb of charge (C) when passing through a power supply EMF = Energy transformed from other forms to electrical / charge Can be written as: o ε (V) = E / Q The terminal potential difference (p.d) is the potential difference across the terminals of a cell o If there was no internal resistance, the terminal p.d would be equal to the e.m.f It is defined as:
o V = IR
Where:
o V = terminal p.d (V)
o I = current (A)
o R = resistance (Ω)
Since a cell has internal resistance, the terminal p.d is always lower than the e.m.f In a closed circuit, current flows through a cell and a potential difference develops across the internal resistance
