electrical basics

1. 100% Clean,
Renewable Energy
and Storage for
Everything
Mark Z. Jacobson
Stanford University

2. Chapter 4:
Electricity Basics

3. Definitions

4. Electricity
• Free flowing movement of charged particles, either
 Negatively-charged electrons
 Negatively-charged ions
 Positively-charged ions
• Electric current
 Flow of electric charge through either air or wire
• Types of electricity
 Static electricity
 Lightning
 Wired electricity

5. Wired Electricity
In a wire, atomic nuclei stay in a fixed position and electrons far from their
nucleus freely move about.
These conduction electrons wander from atom to atom and their movement
constitutes an electric current.
1 C = charge of 6.242 x 1018 electrons
1 A = 1 C/s (1 C of charge passes a given spot in 1 s)
Current (A) = change in charge q (C) per unit time t
i = dq/dt

6. Direct Current vs Alternating Current
• Charges can be + or -. Direction of current = direction of + flow.
• Electrons moving to right means current is flowing to left
• Direct current
 Charge flows at constant rate in one direction.
• Alternating current
 Electrons flows to right then left then right sinusoidally over time
 U.S.: AC current 60 Hz = 60 cycles per second
 Europe: AC current 50 Hz

7. Circuit With Light Bulb, Battery, Switch

8. Drift Velocity
Average speed of the net flow of electrons
As electrons collide with each other, they transfer energy to each
other causing a wave of electricity to travel down a wire at nearly
the speed of light, but electrons themselves move slowly
With AC electricity, electrons reverse direction 60 times per
second (in U.S.), so they barely move at all.

9. Drift Velocity
vd = current / (electrons per unit volume of wire x Coulombs per electron x area of
wire)
Find drift velocity in copper wire of area 3.31x10-6 m2 if current = 20 A
Cu molecular weight 63.55 g/mol; density 8,960 kg/m3; and 1 electron per
atom
e-/m3 = 1 e-/atom x 6.023x1023atoms/mol x 1 mol/63.55 g x 8.96x106 g/m3
= 8.49x1028 electrons per m3
 vd = 20 C/s / (8.49x1028 e-/m3 x 1.602x10-19 C/e- x 3.31x10-6 m2)
= 0.00044 m/s = 1.6 m/hr
Thus, the bulk movement of electrons is slow, but they don’t need to move
fast to carry a large amount of current.

10. Kirchoff’s Current Law
At every instant of time the sum
of the currents flowing into any
node of a circuit must equal the
sum of the currents leaving the
node.

11. Voltage
• = Energy (dw, J) carried by a single charge (dq, C)
• v = dw/dq
• Just as a lifted mass gains potential energy; a charge with its voltage raised gains
electrical energy
• A 12-V battery provides 12 J of energy for every 1 C of charge it stores
• Voltage is measured across components. Voltage across battery is 12 V
• Voltage rises across a battery 12 V and drops across a lightbulb
• Current is measured through components. Current through battery =10 A

12. Kirchoff’s Voltage Law
The sum of voltages around
any loop of a circuit at any time
is zero.
Thus, if a voltage across the
battery (from negative to
positive node) is +12 V, the
voltage across the light bulb is -
12 V.

13. Power
Power (W) = change in energy (J) per unit time
 v=12 V battery delivering i=10 A to a load supplies p=120 W
Energy (J) = integral of power over time. For constant power, it is pDt
 p=120 W over 1 min gives (120 J/s) x 60 s = 7,200 J of energy
p =
dw
dt
=
dw
dq
dq
dt
= vi

14. Resistance
• Resistors drop voltage proportionally to current (which stays
constant)
• v = iR, where R is resistance in Ohms (W)
• The higher the resistance, the lower the current for the same
voltage drop
• i = v/R
• Power dissipated in a resistor (where R must equal v/i)
p = vi = i2
R =
v2
R

15. Resistance Examples
• What is the resistance of a filament in a lamp designed to consume
60 W if the power source is 12 V?
 R = v2 / p = 12 V x 12 V / 60 W = 2.4 W
• What is the current that flows?
 i = p / v = 60 W / 12 V = 5 A
• What is the energy consumed over 100 h?
 E = pDt = 60 W x 100 h = 6 kWh
p = vi = i2
R =
v2
R

16. Resistance in Series
Voltage drop with resistors wired in
series:
v=iR1 + iR2 + iR3 = iRS
Total resistance of R1 and R2 in series
is RS=R1+R2 +R3
Example: Total resistance in the circuit
shown is 1000 W = 1 k W

17. Resistance in Parallel
From Kirchoff‘s Current Law:
i = i1 + i2 = v/R1 + v/R2 = v/RP

 v=i RP
The combined resistance in parallel is
always less than either individual
resistance
R p =
1
1
R1
+
1
R2

18. Capacitor
Device to store electric charge;
also used to smoothen voltage
in DC power lines
Made of two parallel
conducting plates separated by
a non-conducting insulator,
such as air or paper

19. Capacitor
When voltage from battery is
applied, negative charges from
negative side of battery accumulate
on plate attached to that end of wire,
creating a negative charge there.
Electrons from other plate flow to +
terminal of battery, creating +
charge on second capacitor plate.
Charge difference creates an
electric field, where electrostatic
energy stored.

20. Capacitance
Describes ability of a capacitor to store electric charge (energy) in an
electric field (units of Farads, F). If charge on each plate is –q and +q,
respectively, and voltage between plates is v, then capacitance is
If plate area (A) is large relative to distance between (d) plates
 C=e0A/d e0=permittivity in a vacuum (F/m)
The higher the permittivity, the more energy is stored
C =
q
v

21. Current Through, Power in a Capacitor
• Power needed to initiate a capacitor‘s change in voltage with time.
From q=Cv,
• As capacitor storage becomes full (dv/dt=0), current goes to 0 so
light goes out
• If voltage change with time were infinite, then power would also be
infinite, which is impossible
• Capacitors resist rapid changes in voltage and are used to
smoothen DC voltage in power lines
i =
dq
dt
= C
dv
dt
pc = vi = Cv
dv
dt

22. Electromagnetism

23. Electromagnetism
An electrical current flowing through a wire creates a circular
magnetic field around the wire. (Orsted, 1820)
A magnet moving toward or away from a coiled wire along a
circuit creates a fluctuating electric current in the wire. (Faraday)
A fluctuating current in one wire creates a fluctuating magnetic
field that induces a fluctuating current in a second wire (Faraday,
1831).

24. Electromagnetism
Faraday’sAugust 29, 1831
experiment creating a brief current

25. Electromagnetism
Another Faraday experiment to
create a current

26. DC Versus AC Electricity
DC electricity current flows in
one direction. DC current and
voltage are independent of
time. AC electricity current
changes direction and
magnitude with time.

27. AC Generator (Alternator)
Rotation of magnetic field
around set of stationary wire
coils creates AC voltage across
the wire coils. The faster the
shaft turns, the greater the
frequency that the current
alternates.

28. AC Electricity
With AC electricity, current and
voltage switch sign and magnitude
sinusoidally. Top: no phase angle;
Bottom: 30o angle. Phase angles
from capacitors or inductors along
circuit; affect current only
Frequency = number of full waves
per second
U.S.: 60 Hz (60 waves/s); Europe,
50 Hz

29. AC Electricity
Voltage & current vary sinusoidally
v(t) = Vmcoswt
i(t) = Imcos(wt+f)
w=angular freq (rad/s)=2pf
f=frequency (1/s)
Period T=1/f
f=phase angle (rad)=fractional period difference between i(t), v(t) peaks

30. AC Electricity
With AC electricity, v, i are root-mean-square (rms) values and p is an average
value. Thus, 120 V AC is Vrms
v=Vrms=√[(Vm
2cos2wt)avg]=Vm/√2
i=Irms=√[(I2
mcos2 (wt+f))avg]=Im/√2
p=vi=VrmsIrms=Pavg
Find resistance and current for 60 W bulb powered by 120 V AC:
R=v2/p=1202/60=240 W
i=p/v=60/120=0.5 A

31. AC Electricity With Capacitor
• Current leads voltage with capacitor since current must flow
before capacitor shows voltage

32. Inductor
Used with transmission systems to limit abnormal currents
Insulated wire coiled around iron core. When current passes
through coil, it creates magnetic field in which energy is
stored.
Analogous to a capacitor, which store energy in an electric
field
Oppose changes in current by changing voltage proportional
to the change in current with time
v(t)=Ldi(t)/dt, L=inductance (Henrys)

33. AC Electricity With Inductor
Current lags voltage since must supply voltage to inductor before
current flows

34. 3-Phase Electricity
• Smoothens current (reduces flicker) relative to single phase
• Electricity generated by three equally-spaced coils of wire
moving through a magnetic field (left) or a magnetic field
moving through three pairs of coiled wires (right)

35. Reactive Power
Real power
Energy/time used to run a motor or heat a home. It is the result of
a circuit with resistive components only (no capacitors or
inductors).
Reactive power
“Imaginary” power that does not do useful work but moves back
and forth within power lines. Byproduct of an AC system that has
inductors or capacitors and arises due to a phase difference (f)
between voltage and current. It represents the product of Volts x
Amperes that are out of phase with each other

36. Reactive Power
DC circuit: p=iv (active, or real power)
AC circuit
Apparent power S=iv = vector sum
of
Active power p=ivcosf
Reactive power Q=ivsinf
f is phase angle between current and
voltage.
Purely resistant AC circuit (iron, heater,
filament bulbs), f=0, so Q=0 and S=p
Power factor = p/S. Should be >0.95 for
Highest efficiency

37. Reactive Power
Reactive power important for 3 reasons:
1) Smoothens voltage on transmission grid by supplying or
absorbing it
2) A sufficient amount of reactive power is needed to avoid blackouts
3) Transformers, motors, and generators require reactive power to
produce magnetic flux

38. Producing Reactive Power
When capacitors and inductors are not sufficient, generators are
used to supply or absorb reactive power to maintain a constant
voltage (“voltage support”) when voltage is too low or high on the
grid.
Such generators produce reactive power by raising their terminal
voltage. This is accomplished by increasing the magnetic field in
the generator. Such generators have high heat losses so don’t
produce much real power. They are paid for reactive power.

39. Transformers

40. Transformers
In 1882, Edison’s first electric utility (Pearl Street, NYC) used DC
power
DC voltages were low (110 V), currents were high, and power
losses (pw =i2Rw) were high, so voltages dropped significantly along
the thick copper wires
In 1886, Westinghouse introduced the first AC grid (Great
Barrington, Massachusetts) using a single-phase AC generator. He
had purchased the rights to use Lucien Gaulard’s transformer and
hired William Stanley to improve it.
Transformers were used to boost voltage entering transmission
lines in order to reduce current, thus line losses. Voltage was

41. Step-Up and Step-Down Transformer
Transmitting power over long
distances is most efficient with
stepped-up voltages and
stepped-down currents to
minimize i2Rw power losses.
Voltages are then stepped
down and currents stepped up
at the end of the line for
consumers.

42. Step-Up Transformer
• Analogous to toothed gears

43. Transformers
• A transformer steps voltage up or down from a powered coil to
an unpowered coil.
• The AC voltage induced in the unpowered coil equals that in
the powered coil multiplied by the ratio of secondary coil turns
to primary coil turns.
• Transformers don’t work with DC

44. Decreasing Current Reduces Line Losses
Doubling v along a transmission line reduces i by a factor of 2 at same power
since p=vi.
Power loss along a wire,
pw=vwi=i2Rw= (p/v)2Rw
where vw=iRw is the voltage loss across the wire.
 Cutting i in half decreases power loss by a factor of 4.
 Raising end voltage (v) by a factor of 10 decreases line loss by a factor of
100.
Modern systems generate 12-25 kV. Transformers boost that to 100-1000 kV
and down again to 4-35 kV

45. AC Versus DC
In 1887, C.S. Bradley invented 3-phase AC generator.
By 1887, Westinghouse had half the number of AC generating
stations as Edison had DC stations
In 1888, Tesla invented 3-phase AC induction motor, which was
critical for powering equipment on an AC grid.
Westinghouse then hired Tesla to improve AC grid, AC generators,
and AC motors.
In 1891, Westinghouse built first power plant (hydro) to supply AC
electricity over long distance (5.6 km) for a gold mine in Ophir, CO

46. AC Versus DC
Edison declined to invest in AC.
In Nov. 1887, dentist Alfred Southwick asked Edison to support the
use of electricity to execute criminals.
Edison didn’t believe in capital punishment but believed
Westinghouse should be punished: “The most effective of these are
known as alternating machines manufactured principally in this country by
Mr. Geo. Westinghouse, Pittsburgh.” Edison lobbied and succeeded in
having first electric chair use AC (1890)
Edison hired Harold Brown to stoke fears about AC electricity.
Demonstrated electrocution of dogs, horses, calves to audiences.

47. AC Versus DC
By 1891, AC had all but taken over.
DC could operate only a few appliances; AC, many.
AC less expensive and could run on larger, more distant power
supplies.
With adoption of AC at the Chicago World’s Fair in 1893 and at the
New York Niagara Falls power station in 1895, AC completed its
takeover.

48. HVDC Transmission
• High-voltage direct current (HVDC) uses DC for most of the
transmission distance. Obtained by converting HVAC to HVDC
then back to HVAC with thyristor or transistor.
• For long distance (> 600 km), HVDC has lower line losses
than HVAC and costs less.
• For short distance (< 600 km), HVAC costs less because of
greater conversion equipment for HVDC.
• HVDC uses voltages 100 kV to 1,500 kV.

49. 120 V – 240 V Outlets
• Home wall receptor receives 60 Hz AC power at 120 V (110-
125 V). Some appliances (e.g., dryer) require 240 V.
• Transformer on power pole steps down voltage from utility
distribution from 4.16-34.5 kV to 120 V or 240 V.