Topic 5: Electricity
What is current?
-Current is the name for moving charges and the path they follow is called the circuit. -Without a complete circuit, a current cannot be maintained for any length of time. -Current flows THROUGH an object when there is a potential difference ACROSS the object. *Current is defined as the rate of flow of electrical charge (I) Current = charge flowed / time taken I = ΔQ / Δt 1 ampere = 1 coulomb per second (1Cs-1)
What is a magnetic force?
-The force experienced by a magnetic field on a moving charge or an electric current. -The direction of the force is shown by the direction of the field lines -The strength of the force is shown by how close the lines are to one another.
What is an ammeter?
An instrument that measures the electric current through it (goes in series)
What is a voltmeter?
An instrument that measures the potential difference across its ends (goes in parallel)
What is a conductor?
An object or material through which electric current can pass. Examples: -all metals (aluminium, brass) -graphite
What is an insulator?
An object or material which electric current cannot pass through. Examples: - plastics (polythene, nylon, acetate) -rubber -dry wood -glass -ceramics
How can the emf of a battery be measured?
By placing a voltmeter across the battery.
What is the equation that internal resistance is involved with?
ε = I(R+r) R: the resistance of the whole circuit ε: emf (voltage) r: internal resistance
Permeability
μ: permeability μο: permeability of vacuum *There is almost no difference between the permeability of air and the permeability of a vacuum. *There are many possible units for this constant, but the most common ones are: NA-2 or TmA-1 *Permeability and permittivity are related constants *Permeability of a vacuum = 4π x 10^-7 NA-2
What is the equation for resistivity?
ρ = RA ÷ L ρ: resistivity (Ωμ) R: resistance (Ω) A: area (m2) L: length (m)
What is the idea of the potential divider?
( R ÷ x ) = ( I ÷ V ) * R is the resistance you will be looking for * x is the resistance of the resistor you have, I is the current of the whole circuit divided by the number of resistors (so if the current is 4 with 2 resistors, it will be 2 Ω) * V is the voltage as a whole
Resistors in parallel
*A parallel circuit branches and allows the charges more than one possible route around the circuit *I (total) = I1 + I2 + I3 = V/R1 + V/R2 + V/R3 * 1/R(total) = 1/R1 + 1/R2 + 1/R3
Resistors in series
*A series circuit has components connected one after another in a continuous chain. *Current = same everywhere (since charge is conserved) *Total potential difference is shared among the components *Resistance (total) = R1 + R2 + R3
Define magnetic field density
*Another name for the magnetic field strength B *It is the force per unit charge on a charge moving with unit velocity at right angles to the field
Representation of electric fields:
*Done using field lines *At any point in a field... -the direction of the field is represented by the direction of the field lines closest to that point -the magnitude of the field is represented by the number of field lines passing near that point *The parallel field lines between plates mean that the electric field is uniform *Electric field lines: -begin on positive charges and end on negative charges -never cross -are close together when the field is strong
Comparisons between electric fields and magnetic fields
*Electric field Caused by: charges Affects: charges Two types of: charge - positive and negative Simple force rule: like charges repel, unlike charges attract *Magnetic field Caused by: magnets (or electric currents) Affects: magnets (or electric currents) Two types of: poles- North and South Simple force rule: like poles repel, unlike poles attract *Differences: 1. A magnet does not feel a force when placed in an electric field 2. A positive charge does not feel a force when placed stationary in a magnetic field. 3. Isolated charges exist whereas isolated poles do not 4. The Earth itself has a magnetic field. It turns out to be similar to that of a bar magnet with a magnetic South pole near the geometric North pole.
What is electrical resistance?
*Electrical resistance is a property of a material that measures its ability to allow current to flow. *High resistance materials thus hinder current flow and low resistance materials allow easy passage of current. *Electrical resistance is measured in ohms (Ω)
What are Kirchhoff's circuit laws?
*First law: ΣI = 0 (junction) -Algebraic sums of the currents at any junction in the circuit is zero. -The current flowing into a junction must be equal to the current flowing out of a junction *Second law: ΣV = 0 (loop) - Around any loop, the total energy per unit charge must sum to zero. -Any source of potential difference (voltage) within the loop must be completely dissipated across the components of the loop (potential drop across the component) *If the chosen loop direction is from the negative side of a battery to its positive side, this is an increase in potential and the value is positive when calculating the sum. *If the direction around the loop is in the same direction as the current flowing through the component, this is a potential drop and the value is negative when calculating the sum.
Sensors
*Light dependent resistor (LDR): -device whose resistance depends on the amount of light shining on its surface -an increase in light causes a decrease in resistance *Thermistor -a resistor whose value of resistance depends on its temperature -most are semi conducting devices that have a negative temperature coefficient (NTC) -this means that an increase in temperature causes a decrease in resistance. *Both of these devices can be used in potential divider circuits to create sensor circuits. The output potential difference of a sensor circuit depends on an external factor.
What does Ohms law state?
- There is a straight line - The line must pass through the origin - The resistance is constant - All the above shows that, in Ohms law, voltage is proportional to current
Describe charge.
- charge is always conserved - charged objects can be created by friction (electrons are physically moved from one object to another) - in order for the charge to remain on the object, it normally needs an insulator. - total charge before = total charge after (impossible to create a positive charge without an equal negative charge)
Magnetic field in a solenoid
-The magnetic field of a solenoid is very similar to the magnetic field of a bar magnet. -The magnetic field inside the solenoid is constant. -The field does not vary at all inside the solenoid, but this can be experimentally verified near the center of a long solenoid. It does tend to decrease near the ends of the solenoid. B = μ(n/length) x Current Thus the field only depends on: 1. the current, 2. the number of turns per unit length (n/l) 3. the nature of the solenoid core, μ It is independent of the cross-sectional area of the solenoid
What is the right hand grip rule?
-The right-hand grip rule for a current-carrying wire gives the direction of the magnetic field due to the current in the wire. -Right hand thumb: direction of the current -Right hand fingers: direction of field lines
Energy difference in an electric field
-When placed in an electric field, a charge feels a force. This means that if it moves around in an electric field work will be done -As a result, the charge will either gain or lose electric potential energy. Gain in kinetic energy = loss of electric energy 1/2 mv^2 = Eqd mv^2 = 2Eqd v = √( (2Eqd) /m)
Magnetic force is proportional to...
-the magnitude of the magnetic field (B) -the magnitude of the current (I) -the length of the current, L, that is in the magnetic field -the sine of the angle, θ, between the field and the current.
Experimentally, the field in a straight wire is proportional to...
-the value of the current I -the inverse of the distance away fro the wire, r. If the distance away is doubled, the magnetic field will halve. -the field also depends on the medium around the wire. Equation B = μI / 2πr μ: permeability
What does the speed (drift velocity) of electrons in ohmic conductors depend on?
1. Cross-sectional area of conductor 2. Length of conductor 3. Material for which conductor is made 4. Temperature of conductor (all these are the resistance of the conductor) 5. Potential difference (voltage) across the conductor
Explain the reasons for the differences between the electrical properties of the insulating material and the electrical properties of the wire.
1. Current (or conduction) is related to the flow of charge 2. Conductors have a lot of free electrons while insulators have a few free electrons 3. There is a larger current in conductors as there are more free electrons. On the other hand, there is a smaller current in the insulators as there are fewer available electrons.
What is the charge of a single electron?
1.6x10E-19 C (negatively charged) [GIVEN IN THE DATA BOOKLET]
What is an electric battery?
A device consisting of one or more cells joined together. In a cell, a chemical reaction takes place, which converts stored chemical energy into electrical energy. There are two different types of cell: 1. Primary cell Cannot be recharged: chemicals in cell get used in a non-reversible reaction (eg: zinc-carbon and alkaline batteries) 2. Secondary cell Can be recharged: electrical energy is reversible. A reverse electrical current charges the cell allowing it to be reused many times (eg: lead acid car battery, nickel-cadmium and lithium-ion batteries) Charge capacity of a cells how much charge can flow before the cell stops working.
What is a resistor?
A device with constant resistance (in other words an ohmic device)
What is a magnetic field?
A field created by electric currents and moving charges
Magnetic force on a moving charge
A single charge moving through a magnetic field also feels a force in exactly the same way that current feels a force. Force on a moving charge is proportional to: -the magnitude of the magnetic field, B -the magnitude of the charge, q -the velocity of the charge, v -the sine of the angle θ, between the velocity of the charge and the field. F = Bqv sin θ *Since force on a moving charge is always at right angles to the velocity of the charge the resultant motion can be circular.
What is a test charge?
A test charge is a charge with a magnitude so small that placing it at a point has a negligible affect on the field around the point.
What does a potential divider do? (also known as a voltage divider)
A voltage divider is a simple circuit which turns a large voltage into a smaller one. More on: https://www.youtube.com/watch?v=Mn2i3DPI-a4
Define direct current (dc)
Current in which electrons move in the same direction with the same direction with the same average drift speed
Define alternating current (ac)
Current in which electrons oscillate instead of moving with the same drift speeding in the same direction.
What is current related to?
Current is related to the flow of charge.
What does Ohm's Law state?
Definition: *The current through a wire is proportional to the potential difference across it, provided the temperature is unchanged. *Ohm's law effectively states that the resistance, R, is constant - and does not change if current (or voltage) is increased as long as the material is not allowed to heat up. * Metallic conductors obey Ohm's Law. Equation: R = V ÷ I
Define the electric resistance of a wire
Definition: The ratio of the voltage across a device to the current through it. Equation: potential difference across a wire ÷ current through the wire
What is the definition of electric current?
Electric current is defined to be the rate of flow of charge (electrons)
How is the magnetic field strength defined as? (equation)
F = BIL sin θ Unit: Tesla (T) 1T --> 1NA-1m-1 Another possible unit for magnetic field strength: Wbm-2 Another possible term is magnetic field density
What are electrostatic forces?
Forces that exist between all charges: like charges repeal, unlike charges attract.
What is the equation of electric current?
I = q ÷ t I = current q = charge t = time [GIVEN IN THE DATA BOOKLET]
What are ohmic devices?
If current and potential difference are proportional (like the metal at constant temperature) the device is said to be ohmic
Define magnetic field lines
Imaginary curves whose tangents give the magnetic field
What does charge flow depend on?
It depends on the velocity of the charges.
How do you recharge a secondary cell?
It has to be connected to an external DC power source (with a slightly higher pd - voltage)
What is electric potential difference also referred to as? (+ the units)
It is also referred as voltage measured in volts (V)
What is potential difference?
It is an energy difference. Remember: energy difference = energy converted = work done Definition: The electric potential difference between two points is the work done per unit charge in moving a charge from one point to the other Equation: ΔV = work done ÷ charge ΔV = W ÷ q Measured in volts [EQUATION IS NOT GIVEN IN THE DATA BOOKLET]
What is the velocity of the charges called?
It is called drift velocity
What does the law of conservation of charge state?
It is impossible to create a positive charge without an equal negative charge
What is joules ÷ coulomb also known as?
It is known as voltage.
What is the unit of electric current?
It is measured in amps (A)
What is charge measured in?
It is measured in coulombs (C)
What is electrically neutral matter?
Matter that contains equal amount of positive and negative charge
Define convectional current
Motion of a fluid as a result of differences in fluid density. It flows form positive to negative.
What does Ohm's law state?
Ohm's law states that the current flowing through a piece of metal is proportional to the potential difference across it providing the temperature remains constant. In symbols: V proportional to I (temperature is constant) [At constant temperature the current through most metallic conductors is proportional to the voltage across the conductor]
Power dissipation
Potential difference = energy difference / charge flowed Current = charge flowed / time taken potential diff. x current => (energy difference) / (charge flowed) = (charge flowed) / (time taken) = energy difference / time This energy difference per time is the power dissipated by the resistor (all this energy is going to be heating up the resistor) P = V x I Power = voltage x current
When do power supplies deliver maximum power when they have internal resistance?
Power supplies deliver maximum power when the resistance of the external circuit equals the internal resistance of the power supply.
What is the relationship between resistance and diameter in a wire?
Resistance decreases as the diameter increases.
What does Coulomb's law state?
The electric force between two point charges is proportional to the product and inversely proportional to the square of their separation. Equation 1: F = kq1q2 / r^2 = k ( (q1q2) / r^2 ) k: Coulomb constant Equation 2: F = q1q2 / 4πεοr^2 F: force between two point charges 4πεοr^2: constants εο: permittivity of free space (a constant) q1: value of first charge q2: value of second charge k = 1 / 4πεο
Define electric potential energy
The energy that a charge has as a result of its position in an electric field. Electric potential energy = force x distance = Eq x d
What is an electric field?
The field created by electric charges. E = F / q2 = force per unit positive pont test charge. Coulombs law in relation to this: E = q1 / 4πεοr^2
What is resistance?
The mathematical ratio between potential difference and current. If something has a high resistance, it means that you would need a large potential difference across it in order to get current to flow Resistance = potential difference / current R = V / I Unit: ohm (Ω) [which is equal to 1 volt per amp] 1 ohm = 1 VA-1
Define magnetic flux
The product of the component of the magnetic field strength normal to an area
Define resistivity
The resistance of a conductor of unit length and unit cross-sectional area R = ρl/A l = length Units: Ωm The resistivity equation predicts that the resistance R of a substance will be: 1. proportional to the length l of the substance 2.inversely proportional to the cross-sectional area A of the substance
What is the definition of resistance?
The resistance of a material (or device) is the ratio of the voltage across the material to the current flowing through the material. Equation: R = V ÷ I R: resistance V: voltage I: current
What is resistivity?
The resistivity of a material is a measure of the resistance of a certain material.
Define drift velocity
The speed of the electrons due to the current is called drift velocity. -It is possible to estimate the drift velocity of electrons using the generalised drift speed equation. -All currents are comprised of the movement of charge-carriers and these could be positive or negative; not all currents involve just the movement of electrons. Current I = ΔQ / Δt I = nAvq Δt: time the average distance moved by a charge carrier = v x Δt so the volume of charge moved past a point = A x vΔt so the number of charged-carriers moved past a point = n x AvΔt so charge moved past a point ΔQ = q x nAvΔt
Define convection
The transfer of heat in fluids through differences in fluid density.
Define conduction
The transfer of heat through through electron and molecular collisions. As they move, the interactions between the conduction electrons and the lattice ions means that work needs to be done. Therefore, when current flows, the metal heats up.
What is (electric) potential difference?
The work done per unit charge in moving a small point positive charge between two points. Potential difference between two points = energy difference per unit moved = energy difference / charge = work done / charge V = W / q Basic unit: Joules per coulomb (JC-1) -A very important point to note is that for a given electric field, the potential difference between any two points is a single fixed scalar quantity. -The work done between these two points does not depend on the path taken by the test charge. A technical way of saying this is "the electric field is conservative"
Define electromotive force (emf)
The work done per unit charge in moving charge across the terminal of the battery.
Two parallel wire and the ampere
This equation defines the ampere (eq. created by two parallel wires) Magnitude of force per unit length on either wire = μΙ1Ι2 /2πr (N)
Fleming's left hand grip rule
Thumb: force (F) First finger: field (B) Second finger: current (I)
What does energy of a circuit refer to?
To the power of the circuit (they are both measured in watts).
What is a potential divider?
Two resistors 'divide up' the potential difference of the battery. It is also known as a potentiometer. [It is a passive linear circuit that produces an output voltage (Vout) that is a fraction of its input voltage (Vin). Voltage division is the result of distributing the input voltage among the components of the divider]
What is voltage?
Voltage is the quantity that measures the potential energy difference (per unit charge) across two points in a circuit. It is also the quantity that measures the actual potential energy per coulomb of a charge.
What is the motor effect in magnetism?
When a current carrying wire is placed in a magnetic field the magnetic interaction between the two results in a force. (the direction of this force is at right angles to the plane)
When does an electric current flow?
When charged particles move
What are non-ohmic devices?
When current and potential difference are not proportional (like the filament lamp or the diode) are said to be non-ohmic
What is the equation of work done?
Work done = force x distance (measured in Joules)
Graphs that show how the current varies with potential difference for some typical devices: a) metal at constant temperature b)filament lamp c) diode What do they look like?
a) A metal at constant temperature will have a line that goes through the origin (straight line) b) Filament lamp: S shaped graph going through the origin c) Diode: curving upwards (straight in the negative x-axis and turns upwards in the positive part of the x-axis)
What is emf?
emf = electromotive force The work done per unit charged in moving charge across the terminals of a battery. ε = I (R=r) I: current R: external resistance r: internal resistance ε: emf (measured in volts)