Electric Current

Defining Electric Current

 Electric current is the flow of charge carriers and is measured in units of amperes
(A) or amps
 Charge can be either positive or negative
 When two oppositely charged conductors are connected together (by a length of wire),
charge will flow between the two conductors, causing a current

Charge Flowing Between Conductors

Charge can flow between two conductors. The direction of conventional current in a metal is
from positive to negative

 In electrical wires, the current is a flow of electrons

 Electrons are negatively charged; they flow away from the negative terminal of a cell
towards the positive terminal
 Conventional current is defined as the flow of positive charge from the positive terminal
of a cell to the negative terminal
o This is the opposite to the direction of electron flow, as conventional current was
described before electric current was really understood

Conventional Current
 By definition, conventional current always goes from positive to negative (even though
electrons go the other way)

 There are several examples of electric currents, including in household wiring and
electrical appliances
 Current is measured using an ammeter
 Ammeters should always be connected in series with the part of the circuit you wish to
measure the current through

An Ammeter in a Circuit

An ammeter can be used to measure the current around a circuit and always connected in
series

Quantisation of Charge
 The charge on charge carriers is quantised
 Charge comes in definite bits - e.g. a single proton has a single positive charge, whereas
a single electron has a single negative charge
  In this way, the quantity of charge can be quantised dependent on how many protons or
electrons are present - positive and negative charge has a
definite minimum magnitude and always comes in multiples of that magnitude
 This means that if we say something has a given charge, the charge is always a multiple
of the charge of an electron by convention
o The charge of an electron is -1.60 × 10-19 C
o The charge of a proton by comparison is 1.60 × 10-19 C (this is known as the
elementary charge, denoted by e and measured in coulombs (C)

Calculating Electric Current & Charge

Calculating Electric Charge
 Current can also be defined as the charge passing through a circuit per unit time
 Electric charge is measured in units of coulombs (C)
 Charge, current and time are related by the following equation:

Q = It =Ne Where

o Q = charge (C)
o I = current (A)
o t = time (s)
o N=total number of net electrons
o e=elementary charge=1.6x10-19C

Worked example

When will 8 mA of current pass through an electrical circuit?

A. When 1 J of energy is used by 1 C of charge

B. When a charge of 4 C passes in 500 s

C. When a charge of 8 C passes in 100 s

D. When a charge of 1 C passes in 8 s

Answer: B

Step 1: Write out the equation relating current, charge and time

Q = It

Step 2: Rule out any obviously incorrect options

o Option A does not contain charge or time, so can be ruled out

Step 3: Try the rest of the options to determine the correct answer


o Consider option B:

I = 4 ÷ 500 = 8 × 10–3 = 8 mA


o Consider option C:

I = 8 ÷ 100 = 80 × 10–3 = 80 mA


o Consider option D:

I = 1 ÷ 8 = 125 × 10–3 = 125 mA


o Therefore, the correct answer is B

Calculating Current in a Current Carrying Conductor

 In a conductor, current is due to the movement of charge carriers
 These charge carriers can be negative or positive, however the current is always taken to
be in the same direction
 In conductors, the charge carrier is usually free electrons
 In the image below, the current in each conductor is from right to left but the charge
carriers move in opposite directions shown by the direction of the drift speed v
o In diagram A (positive charge carriers), the drift speed is in the same direction as
the current
o In diagram B (negative charge carriers), the drift speed is in the opposite direction
to the current
 Current in a Current Carrying Conductor

The charge carriers move in opposite directions shown by the direction of the drift speed v.

 The drift speed is the average speed the charge carriers are travelling through the
conductor. You will find this value is quite slow. However, since the number density of
charge carriers is so large, we still see current flow happen instantaneously
 The current can be expressed in terms of the number density (number of charge carriers
per unit volume) n, the cross-sectional area A, the drift speed v and the charge of the
charge carriers q

I = Anvq

o I = current (A)
o A = cross-sectional area (m2)
o n = number density of charge carriers (m-3)
o v = average drift speed of charge carriers (ms-1)
o q = charge of each charge carrier (C)
  The same equation is used whether the charge carriers are positive or negative

Potential Difference
 A cell makes one end of the circuit positive and the other negative. This sets up
a potential difference (d) across the circuit
 The potential difference across a component in a circuit is defined as the energy
transferred per unit charge flowing from one point to another
 The energy transfer is from electrical energy into other forms
 Potential difference is measured in volts (V). This is the same as a Joule per coulomb (J
C-1)
o If a bulb has a voltage of 3 V, every coulomb of charge passing through the bulb
will lose 3 J of energy
 The potential difference of a power supply connected in series is always shared between
all the components in the circuit
 Potential Difference in a Series Circuit

The potential difference is the voltage across each component in a circuit

 Potential difference or voltage is measured using a voltmeter

 A voltmeter is always set up in parallel to the component you are measuring the voltage
for

Potential Difference in a Parallel Circuit

Potential difference can be measured by connecting a voltmeter in parallel between two points
in a circuit.

Calculating Potential Difference

 The potential difference is defined as the energy transferred per unit charge
 Another measure of energy transfer is work done
 Therefore, potential difference can also be defined as the work done per unit charge

o V = potential difference (V)

o W = work done (J)
o Q = charge (C)

Worked example

A lamp is connected to a 240 V mains supply and another to a 12 V car battery. Both lamps have
the same current, yet 240 V lamp glows more brightly.

Explain in terms of energy transfer why the 240 V lamp is brighter than the 12 V lamp.

ANSWER:

 Both lamps have the same current, which means charge flows at the same rate in both
 The 240 V lamp has 20 times more voltage than the 12 V lamp
 Voltage is the energy transferred (work done) per unit charge
 This means the energy transferred to each coulomb of charge in the 240 V lamp is 20
times greater than for the 12 V lamp
 This makes the 240 V lamp shine much brighter than the 12 V lam
Electrical Power
Calculating Electrical Power
 In “Work, Energy and Power”, Power P was defined as the rate of doing work
o Potential difference is the work done per unit charge
o Current is the rate of flow of charge
 So, the power dissipated (produced) by an electrical device is defined as:

P = IV


o P = power (W)
o I = current (A)
o V = potential difference/voltage (V)

 Using V = IR to rearrange for either V or I and substituting into the power equation
means we also write power in terms of resistance R

R = resistance (Ω)

 This means for a given resistance for example, if the current or voltage doubles the power
will be four times as great

Worked example

Two lamps are connected in series to a 150 V power supply.

Which statement most accurately describes what happens?

A. Both lamps light normally

B. The 15 V lamp blows

C. Only the 41 W lamp lights

D. Both lamps light at less than their normal brightness

Resistance
Defining Resistance

 Resistance is defined as the opposition to current

o For a given potential difference: The higher the resistance the lower the current

 Wires are often made from copper because copper has a low electrical resistance. This is also
known as a good conductor

 The resistance R of a conductor is defined as the ratio of the potential difference V across to the
current I in it

o R = resistance (Ω)

o V = potential difference (V)

o I = current (A)

 Resistance is measured in Ohms (Ω)

 An Ohm is defined as one volt per ampere

 The resistance controls the size of the current in a circuit

o A higher resistance means a smaller current

o A lower resistance means a larger current

 All electrical components, including wires, have some value of resistance

Calculating Resistance

 To find the resistance of a component, we can set up a circuit like the one shown below
Determining Resistance

 The power supply should be set to a low voltage to avoid heating the component,
typically 1-2 V

 Measurements of the potential difference and current should then be taken from the
voltmeter and ammeter respectively

 Finally, these readings should be substituted into the resistance equation

Worked example

A charge of 5.0 C passes through a resistor of resistance R Ω at a constant rate in 30 s. If the

potential difference across the resistor is 2.0 V, calculate the value of R.
Ohm's Law
 Ohm’s law states that for a conductor at a constant temperature, the current through it
is proportional to the potential difference across it
 Constant temperature implies constant resistance
 This is shown the equation below:

V = IR

o V = potential difference (V)

o I = current (A)
o R = resistance (Ω)

 The relation between potential difference across an electrical component (in this case a
fixed resistor) and the current can be investigated through a circuit such as the one below

Investigating Potential Difference and Current in a Circuit

 Circuit for plotting graphs of current against voltage

 By adjusting the resistance on the variable resistor, the current and potential difference
will vary in the circuit
 Measuring the variation of current with potential difference through the fixed resistor will
produce the straight line graph below

Plotting Current Against Voltage

Circuit for plotting graphs of current against voltage.

 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 obeys 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

Worked example

The current flowing through a component varies with the potential difference V across it as
shown.

Which graph best represents how the resistance R varies with V?

Graphs showing varying gradients
I-V Characteristics
 As the potential difference (voltage) across a component is increased, the current also
increases (by Ohm’s law)
 The precise relationship between voltage and current is different for different components
and can be shown on an I-V graph:

I-V Characteristics of Different Components

I-V characteristics for metallic conductor (e.g. resistor) and semiconductor diode

 The I-V graph for a metallic conductor at constant temperature e.g. a resistor, is very
simple:
o The current is directly proportional to the potential difference
o This is demonstrated by the straight line graph through the origin
 The I-V graph for a semiconductor diode is slightly different. A diode is used in a circuit
to allow current to flow only in a specific direction:
o When the current is in the direction of the arrowhead symbol, this is forward
bias. This is shown by the sharp increase in potential difference and current on
the right side of the graph
o 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 potential difference on the left
side of the graph

Worked example
The I–V characteristic of two electrical component X and Y are shown.

Which statement is correct?

A. The resistance of X increases as the current increases

B. At 2 V, the resistance of X is half the resistance of Y

C. Y is a semiconductor diode and X is a resistor

D. X is a resistor and Y is a filament lamp

ANSWER: C

 The I-V graph X is linear

o This means the graph has a constant gradient. I/V and the resistance is therefore
also constant (since gradient = 1/R)
o This is the I-V graph for a conductor at constant temperature e.g. a resistor
 The I-V graph Y starts with zero gradient and then the gradient increases rapidly
o This means it has infinite resistance at the start which then decreases rapidly
o This is characters of a device that only has current in one direction e.g a
semiconductor diode
 Therefore the answer is C

Resistance in a Filament Lamp

 The I-V graph for a filament lamp shows the current increasing at a proportionally slower
rate than the potential difference
 I-V Characteristics for a Filament Lamp

A graph showing the I-V characteristics for a filament lamp.

 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

Resistance and Temperature

 All solids are made up of vibrating atoms

o The higher the temperature, the faster these atoms vibrate
 Electric current is the flow of free electrons in a material
 The electrons collide with the vibrating atoms which impedes their flow, hence the
current decreases

o So, if the temperature increases, the resistance increases

o And as the resistance increases, the current decreases

Resistivity
 All materials have some resistance to the flow of charge
 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
 Free Electrons and Resistivity

Free electrons collide with ions which resist their flow

 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

 R = resistance (Ω)
 ρ = resistivity (Ωm)
 L = length (m)
 A = cross-sectional area (m2)

 The resistivity equation shows that:

o The longer the wire, the greater its resistance
o The thicker the wire, the smaller its resistance
 Wire Properties and Resistance

The length and width of the wire affect 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
 Resistivity is measured in Ω m

Resistivity of Materials at Room Temperature Table

Material Resistivity ρ/Ωm

Copper 1.7 x 10-8
Metals Gold 2.4 x 10-8
Aluminium 2.6 x 10-8
Germanium 0.6
Semiconductors
Silicon 2.3 x 103
Glass 1012
Insulators
Sulfur 1015

 The higher the resistivity of a material, the higher its resistance

 This is why copper, with its relatively low resistivity at room temperature, is used for
electrical wires — current flows through it very easily
 Insulators have such a high resistivity that virtually no current will flow through them

Worked example
Two electrically-conducting cylinders made from copper and aluminium respectively.

Their dimensions are shown below.

Resistance in Sensory Resistors

 A light-dependent resistor (LDR) is a non-ohmic conductor and sensory resistor
 Its resistance automatically changes depending on the light energy falling onto it
(illumination)
 As the light intensity increases, the resistance of an LDR decreases
 This is shown by the following graph:

LDR Graph

Graph of light intensity and resistance for an LDR

 LDRs can be used as light sensors, so, they are useful in circuits which automatically
switch on lights when it gets dark, for example, street lighting and garden lights
o In the dark, its resistance is very large (millions of ohms)
o In bright light, its resistance is small (tens of ohms)

Resistance of an LDR
 Resistance of an LDR depends on the light intensity falling on it

Worked example

Which graph best represents the way in which the current I through an LDR depends upon the
potential difference V across it?
 As the potential difference across the LDR increases, the current increases causing its
resistance to decrease
 Ohm’s law states that V = IR
 The resistance is equal to V/I, or 1/R = I/V = gradient of the graph
 Since R decreases, the value of 1/R increases, so the gradient must increase
 Therefore, I increases with the p.d with an increasing gradient

Resistance in a Thermistor
 A thermistor is a non-ohmic conductor and sensory resistor
 Its resistance changes depending on its temperature
 As the temperature increases the resistance of a thermistor decreases
 This is shown by the following graph:
 Thermistor Graph

Graph of temperature and resistance for a thermistor

 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

Resistance through a Thermistor

The resistance through a thermistor is dependent on the temperature of it

Worked example

A thermistor is connected in series with a resistor R and a battery.

The resistance of the thermistor is equal to the resistance of R at room temperature.When the
temperature of the thermistor decreases, which statement is correct?

A. The p.d across the thermistor increases

B. The current in R increases

C. The current through the thermistor decreases

D. The p.d across R increases

ANSWER: A

 The resistance of the thermistor increases as the temperature decreases

 Since the thermistor and resistor R are connected in series, the current I in both of them
is the same
 Ohm’s law states that V = IR
 Since the resistance of the thermistor increases, and I is the same, the potential
difference V across it increases
 Therefore, statement A is correct