DC Electricity Flashcards
Define Electric current
Electric current is the rate of flow of charge
I = ∆Q/∆t (change in charge over change in time)
Define Potential difference
The potential difference between two points in a circuit is the electrical energy per unit charge converted into other forms of energy (energy taker)
Define Electromotive force
The electromotive force of an electrical source is defined as the energy per unit charge converted into electrical energy by the source (energy giver)
Give the formula for PD and describe its units
potential difference = work done / charge passing
V = W/Q; W= E(emf)
[V] = [J C^-1]
A volt is a joule per coulomb. There would be a p.d. of 1V between two points in a circuit if 1J of energy is converted when 1C of charge passes between the points
Explain Kirchhoff’s First Law
The algebraic sum of the currents at a junction is equal to zero
∑I = 0
It is based on the conservation of charge
Explain KIrchhoff’s Second Law
The algebraic sum of the emf’s in a circuit is equal to the algebraic sum of the potential differences (in a closed loop)
∑E=∑V=∑IR
It is based on the conservation of energy
How is resistance calculated in series and in parallel
Resistors in series:
Rat=R1+R2+R3 (IRt=IR1+IR2+IR3)
Current is the same in each
Resistors in parallel:
1/Rt=1/R1+1/R2+1/R3 (V/Rt=V/R1+V/R2+V/R3)
Potential difference across each is the same (Current splits into 3)
Define Power
Power is the rate of doing work P=∆W/∆t
So W=QV; W/t = Q/t * V; therefore P=IV
Using V=IR; P=I^2*R and P=(V^2)/R
And P∆t=IV∆t; ∆W=IV∆t=E
Define Resistance and state its unit
The resistance of an electrical component can be thought of as its opposition to an electric current flowing in it
Resistance = Potential Difference/Current; R=V/I
[Ω] Ohm = [V A^-1]
State Ohm’s Law
Ohm’s law states that for metals at a constant temperature, the current in the metal is proportional to the potential difference across it (R=V/I is constant)
Describe a voltmeter, an ammeter and a digital ohmmeter
A voltmeter must take some current to operate, in order to keep the current taken as low as possible voltmeters should have a very high resistance (a perfect would have infinite). Digital voltmeters usually have around 10MΩ, analogue - kΩ. A voltmeter needs to be connected in parallel with the component.
An ammeter should have a very low resistance so that it does not affect the current that it is measuring (a perfect one would have zero). An ammeter needs to be connected in series.
A digital ohmmeter uses a battery which produces a very small current into the component. This current is measured by the meter and then converted into a resistance reading by the ‘electronics’ inside the meter. A digital ohmmeter needs to be connected directly to the component without a circuit.
Recall the current potential difference graphs for different materials
Ohm’s law - straight line
Tungsten filament lamp - f shape
Semiconductor diode - straight line along the X axis until the barrier potentialm, then up
Thermistor - the opposite of the f shape
Define Resistivity
Resistivity (symbol rho) is a property of a material and is defined by the equation R=pl/A. It is constant and depends on the material
This is because resistance is proportional to length and inversely proportional to cross sectional area
How to measure the resistivity of polythene (or any other insulator)?
Polythene is a good insulator so we need the sample to have a short length and large cross-sectional area, to make the resistance as small as possible. We use a high voltage to try and get a measurable current. To pass the current through we put the polythene sheet in between two metal plates.
What are the resistivities for different types of materials?
Conductors ~ 10^-8
Semiconductors ~ 10^-5 - 10^3
Insulators ~ 10^10 - 10^16
How can a rheostat be used?
A rheostat can be used to vary current or as a potential divider (potentiometer) to vary p.d.
Using the potentiometer method is more useful as you can get a much greater variation of p.d.’s from zero up to p.d. of the battery.
So a rheostat (three-terminal variable resistor) with a sliding contact can be thought of as 2 resistors connected in series.
The potential difference is divided in the ratio of the resistances.
Explain the concepts of emf and internal resistance
The reading on the voltmeter directly connected to a cell is not the same as the emf of the cell because there is a p.d. across the internal resistance (r) of the battery.
So, using KIrchhoff’s second law:
∑E=∑IR; E=IR+Ir; E=V+Ir; V=E-Ir
V=-rI+e
How does the resistance of metals change with temperature?
Metals have a positive temperature coefficient, so resistivity increases with temperature increase
Using I=nAvq, A and q are constant for a given wire. For a metallic conductor n does not depend on the temperature, so n is also constant. As temperature increases, the increased vibrations of the lattice reduce the drift velocity v, of the electrons, and so I will also decrease, so resistance increases.
How does the resistance of semiconductors/thermistors change with temperature?
Semiconductors/thermistors have a negative temperature coefficient, resistivity decreases when temperature increases.
Using I=nAvq, in a semiconductor, an increase in temperature can provide extra energy to release more charge carriers. This means n increases exponentially with the absolute temperature, so n increases by much more than the relatively small decrease in v. The overall effect is that I increases, so the resistivity decreases with temperature.
Explain I=nAvq
A current in a wire is due to conduction electrons moving in the opposite direction to the conventional current.
In a metallic conductor the charge carriers are loosely bound outer electrons - so called ‘free’ or ‘delocalised’ electrons. These electrons move with random thermal motion, to and fro within the crystal lattice of the metal at speeds approaching one thousandth the speed of light. They are also mainly responsible for metals being good conductors of heat. When a p.d. is applied to a circuit an electric field is created and exerts a force on the free electrons, causing them to drift in the direction of the force. In accordance with Newton’s second law, the electrons would accelerate continuously if it were not fro the fact that they collide with the regularly spaced atoms in the lattice. These atoms are positive ions because the free electrons are detached from the atoms, leaving them with a positive charge. These collisions cause an equal and opposite force to be exerted on the electrons, which, by Newton’s first law, continue with a constant drift velocity, giving rise to a constant current.
So volume of wire = A*l
There are n conduction electrons in 1 m^3
So nAl conduction electrons in Al m^3
Charge on 1 electron = e or q
These electrons will pass through l m in l/v s (v - drift velocity)
I=∆Q/∆t; I = (nAlq)/(l/v); I = nAvq
