Electric Circuits Flashcards
Define current, and give the equation that comes from this definition.
Current is the rate of flow of charge
I = Q / t
“Q” is the amount of coulombs.
Define potential difference, and give the equation that comes from this definition.
Potential difference is the energy transferred/work done per coulomb of charge.
V = W / Q
1V is when 1J of energy is transferred per coulomb of charge.
What is resistance? What equation is used to find resistance?
How difficult it is for current to flow. Could be defined as potential difference per unit of current.
R = V / I
What are charge carriers?
A charge carrier is a charged particle that is free to move. Examples of charge carriers are electrons and ions.
State Kirchoff’s first law. State what quantity is conserved
The total charge/current entering a point will equal the total charge/current leaving the point.
Charge is conserved.
State Kirchoff’s second law. State what quantity is conserved
The total emf in a closed circuit will equal the sum of the potential differences across each component.
Energy is conserved.
When deriving formulae for combining resistors in series and parallel, what must you start with?
Always start with the conservation law, either write:
Charge is conserved, so QT = Q1 + Q2 + Q3 so current is conserved, IT = I1 = I2 = I3 = …
Energy is conserved, therefore ε = V1 + V2 + V3
Derive the formula for the total resistance in a series circuit
Energy is conserved.
ε = VT = V1 + V2 + V3
ε = IRT = IR1 + IR2 + IR3
IRT = IR1 + IR2 + IR3
RT = R1 + R2 + R3
Derive the formula for the total resistance in a parallel circuit
Charge is conserved.
QT = Q1 + Q2 + Q3
Q/t = I
IT = I1 + I2 + I3
Voltage is the same in all branches (ε)
I = ε/R
ε/RT = ε/R1 + ε/R2 + ε/R3 ε/RT = ε/R1 + ε/R2 + ε/R3
1/ Rt = 1/ R1 + 1/ R2 + 1/ R3
Define power.
Power is the rate of energy transfer. Measured in Watts.
List all equations that could be used to calculate power and energy in circuits and/or components.
P = IV
P = W / t
P = I^2 R
P = V^2 / R
Derive the equations P=I^2R and P=V^2/R.
P = IV and V = IR
If V = IR is substituted for V:
P = I (IR) = I^2 R
If I=V/R is substituted for I:
P = (V / R)V = V^2 / R
How does the gradient of the graphs below give you resistance:
a) I-V graphs (I on x axis)
b) V-I graphs (V on x axis)
For an I-V graph the resistance is given by the gradient.
For a V-I graph the resistance is given by 1 / gradient
State Ohm’s law.
Current is directly proportional to potential difference.
What is an ohmic conductor. Give examples.
An ohmic conductor is a component where current and potential difference are directly proportional.
A resistor or wire at a constant temperature is an ohmic conductor.
Interpret the I-V graph for an ohmic resistor.
A straight positive line through the origin
At constant temperature, the current through a metallic conductor is directly proportional to potential difference.
The fact the line passes through the origin shows the resistance doesn’t change.
The shallower the gradient, the greater the resistance of the conductor.
Metallic conductors are ohmic.
Interpret the I-V graph for a filament lamp.
A curve through the origin that decreases over time and is reflected to the negative side.
As potential difference increases, energy
increases ∴ the velocity of the electrons increases ∴ more energy is transferred when they collide with lattice ions ∴ the temperature of the metal lattice ions increase ∴ the amplitude of the vibrations of metal lattice ions increases ∴ the chance of collisions increases ∴ resistance increases.
This means less current can flow, so the graph curve decreases.
Interpret the I-V graph for an NTC thermistor.
A curve through the origin that increases over time and is reflected to the negative side.
As voltage increases, the current increases. More current leads to an increase in temperature therefore a decrease in resistance. This means more current can flow, so the graph curve increases.
Interpret the I-V graph for a diode.
An exponential graph with a curve at around 0.6V.
The current is allowed to flow forward bias. Most diodes require a threshold voltage of about 0.6V in the forward direction before they will conduct. In reverse bias, the resistance of the diode is very high and the current that flows is very thin.
Describe in detail how the resistivity of a metal changes with temperature.
Charge is carried through metals by free electrons in a lattice of positive ions.
Heating up a metal makes it harder for electrons to move about. The lattice of ions vibrate more when heated, meaning the electrons collide with them more frequently, therefore transferring some of their kinetic energy into other forms.
When kinetic energy is lost by the individual electrons, their speed and therefore the mean drift velocity decreases. As current is proportional to drift velocity, I = nqvA, this means the current in the wire decreases so its resistance and resistivity increases.
Give examples of components that are semiconductors.
Thermistors, LDRs and Diodes.
Explain how a negative temperature coefficient thermistors work in detail.
In an NTC thermistor, increasing temperature decreases resistance. Increasing the temperature of the thermistor gives more electrons enough energy to escape from their atoms. This means that there are more charge carriers available so current increases and resistance decreases.
Explain how LDRs work in detail.
The greater the intensity of the light the lower the resistance. Light provides the energy to release more electrons so there are more charge carriers. This results in a higher current and a lower resistance.
What does the temperature-resistance graph look like for a NTC thermistor?
A negative exponential graph.
What does the temperature-light intensity graph look like for a LDR?
A negative exponential graph.
How is mean drift velocity different to the speed of individual electrons.
The mean drift velocity is the average velocity of all the charge carriers. Charges move randomly in all directions but will tend to drift one way so the speed of a particular electron at any given instant can be very different to the mean drift velocity.
What is drift velocity?
The average velocity of all the charge carriers in a circuit.
How can you calculate drift velocity?
I = n A v q
“I” is current.
“n” is the number density of charge carriers.
“A” is the cross sectional area of the wire.
“v” is the drift velocity.
“q” is the charge on each charge carrier.
Why do different materials have different resistances?
Different materials have different numbers of charge carriers.
State how metals, semiconductors and insulators differ in terms of n (number density of charge carriers).
Metals have the highest value for n as they have free electrons so lots of charge carriers.
Semi-conductors have fewer charge carriers so n is lower.
A perfect insulator would not have any charge carriers so n would be zero but in reality insulators have a very small value for n.
State what affects the resistivity of a material, giving the equation and units.
Resistivity is affected by temperature so you can only find the resistivity of a material at a certain temperature.
The equation for resistivity is:
R = pL / A
“R” is resistance.
“p” is resistivity.
“L” is the length.
“A” is the cross-sectional area.
Define resistivity.
The resistance of a sample of the material 1m long with 1m^2 cross sectional area
How is resistance and resistivity different?
Resistance depends on resistivity but also on length and cross-sectional area, whereas resistivity is a property of a material at a particular temperature.
How is resistivity affected by temperature?
As temperature increases resistivity will decrease.
How does the potential along a uniform current-carrying wire vary with the distance along it?
The resistance of a wire is directly proportional to length. Resistance is directly proportional to potential difference.
Therefore, potential difference is directly proportional to the length of the wire.
What is a potential divider?
A potential divider is a circuit that produces an output voltage that is a fraction of the input voltage.
What is the equation used to calculate potential differences and resistances in a potential divider circuit?
V(out) = V(in) x (R1 / (R1 + R2))
Describe how resistance / V changes in a potential divider circuit with a variable resistor.
As the resistance of the variable resistor is increased it will receive a greater share of the voltage so Vout will increase. You can also ‘load’ it further by adding in resistors in parallel.
Describe how a potential divider circuit with a thermistor changes with environmental change.
As the temperature increases the resistance of the thermistor decreases so the fixed resistor receives a bigger share of the voltage.
At high temperatures V(out) is high so this circuit could be used for air conditioning.
If you wanted a heater circuit you could have V(out) over the thermistor instead of the fixed resistor.
How is a potentiometer similar to a potential divider?
A potentiometer allows you to vary V(out).
Define emf.
The total energy supplied/work done by the cell to each unit charge. This is before any energy is transferred within the cell or the wires.
Define terminal potential difference.
This is the total energy available per coulomb of charge to the external circuit. This is after energy has been wasted as lost volts within the cell.
Define internal resistance.
As electrons move through a cell/battery there are collisions with atoms inside the cell. When they collide, some energy is transferred.
Internal resistance is the resistance which must be overcome within the battery itself.
This is why the voltage supplied to the circuit is less than the emf.
What are lost volts?
The voltage ‘lost’ due to the internal resistance.
State the equations for internal resistance.
ε = V + v
ε = I(R + r)
V = ε – v
ε = V + Ir
“ε” is the emf.
“V” is the terminal potential difference.
“I” is the current.
“V” is the lost volts.
“R” is the external resistance.
“r” is the internal resistance.
Give the equation for calculating the total emf of cells in series.
The total emf for cells in series is simply the sum of each of the individual emfs. ε = ε1 + ε2 + ε3 + …
Give the equation for calculating the total emf of cells in parallel.
If cells are connected in parallel the total emf is the same as the emf of one cell. ε = ε1 = ε2 = ε3 = …
Describe the “CPAC 2: Determine the electrical resistivity of a material.” experiment.
Describe the “CPAC 3: Determine the emf and internal resistance of an electrical cell.” experiment.
