Chapter 9 - Electricity and Electric Circuits Flashcards
Equation: force of electric field
F = qE
What is meant by electron drift?
Electrons flow through a conductor and experience random motion at great speeds. When an electric field is applied, the electrons also experience a small net movement in the opposite direction.
Equation: drift velocity of e-
Vd = L/t
What is meant by electric current?
It is the flow of charge from one point to another point over a certain time.
Equation: current (I) in terms of charge
I = Δq/Δt
What is the unit of current?
ampere (A) = C/s
Charge-wise, in which direction does current flow?
Current flows in the same direction in which positive charges flow along a conductor.
How does current flow relate to electrical potential?
Current moves from regions of higher electrical potential to regions of lower electrical potential.
In physics, what are the anode and cathode of a battery?
The anode is negatively charged, while the cathode is positively charged.
What is an electromotive force (emf/ε)?
It is the “force” that can move a charge from a lower potential to a higher potential in a device that has a separation of charge between two points.
What are the units of electromotive force?
volt = V = J/C
Battery symbol (single and multiple)
The second diagram shows multiple cells in series.
What is the resistivity (ρ) of a material? How does it differ in conductors vs insulators?
a measure of how difficult it is for charges to conduct through the material
Insulators: high resistivity
Conductors: low resistivity
Equation: resistivity (ρ) in terms of electric field
ρ = E/J
E = electric field
J = current density
What are the units of resistivity?
V•m/A
*V/A = ohm (Ω)
Ω•m
What is the conductivity (σ) of a material?
It is the reciprocal of resisitivity.
Equation: conductivity (σ)
σ = 1/ρ
ρ = resistivity
What are the units for conductivity?
1/(Ω•m)
Equation: electrical resistance (R) through a wire
R = ρ(L/A)
What are the units of resistance?
ohm (Ω) = V/A
How does the width of a conductor affect electron flow?
Electrons can get through a wider conductor more easily.
Equatin: Ohm’s Law of voltage
V = IR
I = current
R = resistance
In a battery, is the cathode or anode typically at a higher potential?
cathode
As a charge moves through a circuit, the potential increase in the emf (ε) is equal to what?
the potential drop (VAB) as the charge moves through the resistor
Equation: potential drop in terms of internal resistance (r)
VAB = ε - I•r
ε = electromotive force (emf)
I = current
r = internal resistance
Equation: current in terms of emf
I = ε/(R+r)
What is power?
the rate of conversion of electrical potential energy into some other type of energy
Equation: power in terms of PE
P = ΔPEq/Δt
What are the units of power?
watt (W) = J/s
Equation: potential drop in terms of potential energy
VAB = ΔPEq/q
Equation: change in electrical potential energy in terms of voltage
ΔPEq = qV
Equation: power in terms of charge
P = ΔqV/Δt
Equation: power in terms of current (2 versions)
P = IV = I2R
I = currrent
V = voltage
Equation: power in terms of resistance (two versions)
P = V2/R = I2R
What is a capacitor?
two conductors separated by an insulator
What is the capacitance (C) of a capacitor?
the amount of charge that can be stored per volt of potential difference across the two plates
Capacitor symbol
Equation: capacitance (C) in terms of voltage
C = q/V
q = charge
V = potential difference voltage
Equation: capacitance (C) in terms of capacitor structure (2 versions)
C = κ/4πk (A/d) = ε0(A/d)
k = dielectric constant = 9.0 x 109 N•m2/C2
A = area of plates
d = distance between plates
κ = dielectic constant of insulator
What is a dielectric?
an insulator between conducting plates of a capacitor
Equation: capacitor charge in terms of voltage
q = CV
C = capacitance
V = voltage
Equation: capacitor charge in terms of dielectric constant
q = κCvacuumV
κ = dielectric constant
C = capacitance
V = potential difference voltage
What is dielectric breakdown?
If a large electric field exists in a capacitor, the dielectric insulator may ionize, resulting in its cations being attracted to the anode and anions being attracted to the cathode. Conduction of current can then occur.
Equation: electrical potential energy need to charge a capacitor in terms of average voltage
ΔPEq = qVavg = q(1/2V)
Why does a capacitor have a limit to its ability to charge?
As positive charges flow to one plate and build up on that plate, subsequent positive charges are repulsed. Repulsion begins to offset voltage, so no more charge or current is able to flow across the capacitor.
Equation: electrical potential energy need to charge a capacitor in terms of capacitance (3 versions)
ΔPEq = 1/2CV2 = q2/2C = 1/2QV2
What is an RC series circuit?
a circuit that has a resistor and capacitor in series
Equation: voltage in RC series circuit
V = VR + VC = IR + q/C
VR = resistor voltage
VC = capacitor voltage
Equation: current in RC series circuit
I = IR - IC = V/R - q/RC
IR = resistor current
IC = capacitor current
Equation: current through a capacitor in terms of the time constant
I = Ii(e-t/RC)
Ii = initial current
RC = time constant
Equation: charge on a capacitor in terms of the time constant
q = qf(1 - e-t/RC)
qf = final charge
RC = time constant
How does capacitor and resistor size affect the charging/discharging time of a capacitor?
The larger the capacitor, the longer the time it takes to charge/discharge because it can hold more charge.
The larger the resistor, the longer the time it takes the capacitor to charge/discharge because current flow is reduced.
Describe Kirchhoff’s Loop Rule
The sum of potential differences (voltage changes) across any closed circuit (loop) is equal to zero. Vdrop = -IR = emf (ε)
Describe Kirchhoff’s Junction Rule
When a circuit contains multiple loops, the current will divide at junctions. The total current flowing through the pathways leaving a junction must equal the current that entered the junction.
What is meant by a circuit in series?
The circuit elements are in a direct path.
What is meant by a circuit in parallel?
The circuit elements are part of different pathways.
Equation: resistance in series
Req = R1 + R2 + R3…
Describe current in series.
It is the same throughout the circuit - each resistor experiences the same current.
Equation: resistance in parallel
1/Req = 1/R1 + 1/R2 + 1/R3…
Equation: capacitance in parallel
Ceq = C1 + C2 + C3…
Equation: capacitance in series
1/Ceq = 1/C1 + 1/C2 + 1/C3…
Describe current in parellel.
It is different through the circuit - each resistor experiences a different current.
Describe voltage drop in parallel.
It is the same throughout the circuit - each resistor has the same voltage drop.
Describe voltage drop in series.
It changes over the circuit - each resistor causes a different voltage drop.
Equation: resistance in parallel/capacitors in series shortcut (only for 2 elements)
Req = (R1•R2)/(R1 + R2)
Ceq = (C1•C2)/(C1 + C2)
In series, how does the addition of resistors affect the overall resistance?
It increases Req.
In series, how does the addition of capacitors affect the overall capacitance?
It decreases Ceq.
In parallel, how does the addition of capacitors affect the overall capacitance?
It increases Ceq.
In parallel, how does the addition of resistors affect the overall resistance?
It reduces Req.
In series, how is power affected by resistance?
more resistance = more power drain
In parallel, how is power affect by resistance?
more resistance = less power drain
Why is alternating current typically used instead of direct current?
- greater efficiency in that it loses less heat
- safer in that there are brief instances where current and voltage are zero, making it easier to let go
Equation: average power in alternating current
Pavg = IrmsVrms
Equation: root-mean-square current
Irms = Imax/√2
Equation: root-mean-square voltage
Vrms = Vmax/√2
