ELECTRIC CIRCUITS IMETRIC PREFIX TABLEMetricPrefixSymb.docx

ELECTRIC CIRCUITS I
METRIC PREFIX TABLE
Metric
Prefix
Symbol
Multiplier
(Traditional Notation)
Expo-
nential
Description
Yotta
Y
1,000,000,000,000,000,000,000,000
1024
Septillion
Zetta
Z
1,000,000,000,000,000,000,000
1021
Sextillion
Exa
E
1,000,000,000,000,000,000
1018
Quintillion
Peta
P
1,000,000,000,000,000
1015
Quadrillion
Tera
T
1,000,000,000,000

1012
Trillion
Giga
G
1,000,000,000
109
Billion
Mega
M
1,000,000
106
Million
kilo
k
1,000
103
Thousand
hecto
h
100
102
Hundred
deca
da
10
101
Ten
Base
b
1
100
One
deci
d
1/10
10-1

Tenth
centi
c
1/100
10-2
Hundredth
milli
m
1/1,000
10-3
Thousandth
micro
µ
1/1,000,000
10-6
Millionth
nano
n
1/1,000,000,000
10-9
Billionth
pico
p
1/1,000,000,000,000
10-12
Trillionth
femto
f
1/1,000,000,000,000,000
10-15
Quadrillionth
atto
a
1/1,000,000,000,000,000,000
10-18
Quintillionth

zepto
z
1/1,000,000,000,000,000,000,000
10-21
Sextillionth
yocto
y
1/1,000,000,000,000,000,000,000,000
10-24
Septillionth
4-BAND RESISTOR COLOR CODE TABLE
BAND
COLOR
DIGIT
Band 1: 1st Digit
Band 2: 2nd Digit
Band 3: Multiplier
(# of zeros
following 2nd digit)
Black
0

Brown
1
Red
2
Orange
3
Yellow
4
Green
5
Blue
6
Violet
7
Gray
8
White
9
Band 4: Tolerance
Gold
± 5%
SILVER
± 10%
5-BAND RESISTOR COLOR CODE TABLE
BAND

COLOR
DIGIT
Band 1: 1st Digit
Band 2: 2nd Digit
Band 3: 3rd Digit
Band 4: Multiplier
(# of zeros
following 3rd digit)
Black
0
Brown
1
Red
2
Orange
3
Yellow
4
Green
5
Blue
6
Violet

7
Gray
8
White
9
Gold
0.1
SILVER
0.01
Band 5: Tolerance
Gold
± 5%
SILVER
± 10%
EET Formulas & Tables Sheet
Page
1 of
21
UNIT 1: FUNDAMENTAL CIRCUITS
CHARGE
Where:
Q = Charge in Coulombs (C)
Note:
1 C = Total charge possessed by 6.25x1018 electrons
VOLTAGE

Where:
V = Voltage in Volts (V)
W = Energy in Joules (J)
CURRENT
Where:
I = Current in Amperes (A)
t = Time in seconds (s)
OHM’S LAW
Where:
R = Resistance in Ohms (Ω)
RESISTIVITY
Where:
ρ = Resistivity in Circular Mil – Ohm per Foot (CM-Ω/ft)
A = Cross-sectional area in Circular Mils (CM)
ɭ = Length in Feet (ft)
Note:
CM: Area of a wire with a 0.001 inch (1 mil) diameter

CONDUCTANCE
Where:
G = Conductance in Siemens (S)
CROSS-SECTIONAL AREA
Where:
A = Cross-sectional area in Circular Mils (CM)
d = Diameter in thousandths of an inch (mils)
ENERGY
Where:
W = Energy in Joules (J). Symbol
is an italic
W.
P = Power in Watts (W). Unit
is not an italic W.
t = Time in seconds (s)
Note:

1 W = Amount of power when 1 J of energy
is used in 1 s
POWER
Where:
P = Power in Watts (W)
V
= Voltage in Volts (V)
Note:
Ptrue = P in a resistor is also called true power
OUTPUT POWER
Where:
POUT = Output power in Watts (W)
PIN = Input power in Watts (W)
PLOSS = Power loss in Watts (W)
POWER SUPPLY EFFICIENCY
Where:
POUT = Output power in Watts (W)
PIN = Input power in Watts (W)
Efficiency = Unitless value
Note:
Efficiency expressed as a percentage:

UNIT 2: SERIES CIRCUITS (R1, R2, , Rn)
TOTAL RESISTANCE
Where:
RT = Total series resistance in Ohms (Ω)
Rn
= Circuit’s last resistor in Ohms (Ω)
KIRCHHOFF’S VOLTAGE LAW
Where:
VS = Voltage source in Volts (V)
Vn = Circuit’s last voltage drop in Volts (V)
VOLTAGE – DIVIDER
Where:
Vx = Voltage drop in Ohms (Ω)
Rx
= Resistance where Vx occurs in Ohms (Ω)
RT = Total series resistance in Ohms (Ω)

VS
= Voltage source in Volts (V)
TOTAL POWER
Where:
PT = Total power in Watts (W)
Pn = Circuit’s last resistor’s power in Watts (W)
UNIT 3: PARALLEL CIRCUITS (R1||R2||||Rn)
TOTAL RESISTANCE
Where:
RT = Total parallel resistance in Ohms (Ω)
Rn
= Circuit’s last resistor in Ohms (Ω)
TOTAL RESISTANCE - TWO RESISTORS IN PARALLEL
Where:

TOTAL RESISTANCE - EQUAL-VALUE RESISTORS
Where:
R = Resistor Value in Ohms (Ω)
n = Number of equal value resistors (Unitless)
UNKNOWN RESISTOR
Where:
Rx = Unknown resistance in Ohms (Ω)
RA = Known parallel resistance in Ohms (Ω)
KIRCHHOFF’S CURRENT LAW
Where:
n = Number of currents into node (Unitless)
m = Number of currents going out of node (Unitless)
CURRENT – DIVIDER

Where:
Ix = Branch “x” current in Amperes (A)
Rx = Branch “x” resistance in Ohms (Ω)
IT = Total current in Amperes (A)
TWO-BRANCH CURRENT – DIVIDER
Where:
I1 = Branch “1” current in Amperes (A)
R2 = Branch “2” resistance in Ohms (Ω)
R1 = Branch “1” resistance in Ohms (Ω)
TOTAL POWER
Where:
PT = Total power in Watts (W)
Pn = Circuit’s last resistor’s power in Watts (W)
OPEN BRANCH RESISTANCE
Where:
ROpen = Resistance of open branch in Ohms (Ω)
RT(Meas) = Measured resistance in Ohms (Ω)
GT(Calc) = Calculated total conductance in Siemens (S)
GT(Meas) = Measured total conductance in Siemens (S)
Note:
GT(Meas) obtained by measuring total resistance, RT(Meas)

UNIT 4: SERIES - PARALLEL CIRCUITS
BLEEDER CURRENT
Where:
IBLEEDER = Bleeder current in Amperes (A)
IRL1 = Load resistor 1 current in Amperes (A)
IRL2 = Load resistor 2 current in Amperes (A)
THERMISTOR BRIDGE OUTPUT
Where:
= Change in output voltage in Volts (V)
= Change in thermal resistance in Ohms (Ω)
R = Resistance value in Ohms (Ω)
UNKNOWN RESISTANCE IN A WHEATSTONE BRIDGE
Where:
RX = Unknown resistance in Ohms (Ω)
RV = Variable resistance in Ohms (Ω)
R2 = Resistance 2 in Ohms (Ω)
R4 = Resistance 4 in Ohms (Ω)

UNIT 5: MAGNETISM AND ELECTROMAGNETISM
MAGNETIC FLUX DENSITY
Where:
B = Magnetic flux density in Tesla (T)
= Flux in Weber (Wb)
(Greek letter Phi)
A = Cross-sectional area in square meters (m2)
Note:
Tesla (T) equals a Weber per square meter (Wb/m2)
RELATIVE PERMEABILITY
Where:
= Relative permeability (Unitless)
(Greek letter Mu)

= Permeability in Webers per Ampere-turn · meter
(Wb/At·m)
= Vacuum permeability in Webers per Ampere-
turn · meter (Wb/At·m)
Note:
= Wb/ At·m
RELUCTANCE
Where:
R = Reluctance in Ampere-turn per Weber (At/Wb)
ɭ = Length of magnetic path in meters (m)
µ = Permeability in Weber per Ampere-turn · meter
(Wb/At · m)
A = Cross-sectional area in meters squares (m2)
MAGNETOMOTIVE FORCE
Where:
Fm = Magnetomotive force (mmf) in Ampere-turn (At)
N
= Number of Turns of wire (t)
MAGNETIC FLUX

Where:
= Flux in Weber (Wb)
Fm = Magnetomotive force in Ampere-turn (At)
R = Reluctance in Ampere-turn per Weber (At/Wb)
MAGNETIC FIELD INTENSITY
Where:
H = Magnetic field intensity in Amperes-turn per
meter (At/m)
Fm = Magnetomotive force in Ampere-turn (At)
ɭ = Length of material in meters (m)
INDUCED VOLTAGE
Where:
vind = Induced voltage in Volts (V)
B = Magnetic flux density in Tesla (T)
ɭ = Length of the conductor exposed to the magnetic
field in meters (m)
v = Relative velocity in meters per second (m/s)
Note:
Tesla (T) equals a Weber per square meter (Wb/m2)
FARADAY’S LAW

Where:
N = Number of turns of wire in the coil (Unitless)
= Rate of change of magnetic field with respect
to the coil in Webers per second (Wb/s)
ELECTRIC CIRCUITS II
UNIT 1: ALTERNATE CURRENT & INDUCTORS
ALTERNATE CURRENT
FREQUENCY & PERIOD
Where:
f = Frequency in Hertz (Hz)
T = Period in Seconds (s)
Note:
1 Hertz = 1 cycle per 1 second
PEAK TO PEAK VOLTAGE
Where:
Vpp = Peak to peak voltage in Volts (V)
Vp = Peak voltage in Volts (V)
ROOT MEAN SQUARE (RMS) VOLTAGE

Where:
Vrms = Root mean square voltage in Volts (V)
HALF-CYCLE AVERAGE VOLTAGE
Where:
Vavg = Half-cycle average voltage in Volts (V)
RADIAN & DEGREE CONVERSION
Where:
Rad = Number of radians in Rad (rad)
Degrees = Number of degrees in Degrees (0)
Note:
= 3.1416 (Greek letter Pi)
GENERATOR OUTPUT FREQUENCY
Where:

Number of pole pairs = Number of pole pairs (Unitless)
rps = Revolutions per second in Revolutions per
Second (rps)
PEAK TO PEAK CURRENT
Where:
Ipp = Peak to peak current in Amperes (A)
Ip = Peak current in Amperes (A)
ROOT MEAN SQUARE (RMS) CURRENT
Where:
Irms = Root mean square current in Amperes (A)
HALF-CYCLE AVERAGE CURRENT
Where:
Iavg = Half-cycle average current in Amperes (A)
SINE WAVE GENERAL FORMULA
Where:

y = Instantaneous voltage or current value
at angle in Volts or Amperes (V or A)
(Greek letter Theta)
A = Maximum voltage or current value in Volts or
Amperes (V or A)
= Angle where given instantaneous voltage or
current value exists
SINE WAVE LAGGING THE REFERENCE
Where:
Amperes (V or A)
= Angle sine wave is shifted right (lagging) of
reference (Greek letter Phi)
ANGULAR VELOCITY
Where:
= Angular velocity in Radians per second (rad/s)
(Small Greek letter omega)
Note:
= 3.1416
SINE WAVE VOLTAGE

Where:
v = Sinusoidal voltage in Volts (V)
t = Time in Seconds (s)
Note:
= 3.1416
PULSE WAVEFORM AVERAGE VALUE
Where:
vavg = Pulse waveform average value in Volts (V)
baseline = Baseline in Volts (V)
duty cycle = Percent duty cycle in Percent/100%
(Unitless)
Amplitude = Amplitude in Volts (V)
SINE WAVE LEADING THE REFERENCE
Where:
Amperes (V or A)
= Angle sine wave is shifted left (leading) of

reference
PHASE ANGLE
Where:
= Angle sine wave is shifted in Radians (rad)
= Angular velocity in Radians per second (rad/s)
DUTY CYCLE
Where:
Percent duty cycle = Percent duty cycle in Percentage (%)
tw = Pulse width in Seconds (s)
T = Period in Seconds (s)
F = Frequency in Hertz (Hz)

INDUCTORS
INDUCED VOLTAGE
Where:
L = Inductance in Henries (H)
= Time rate of change of the current in Amperes
per second (A/s)
INDUCTANCE OF A COIL
Where:
L = Inductance of a coil in Henries (H)
N = Number of turns of wire (Unitless)
= Permeability in Henries per meter (H/m)
A = Cross-sectional area in Meters squared (m2)
= Core length in Meters (m)
Notes:
Permeability in H/m is equal to Wb/At·m
Non-magnetic core = Permeability of a vacuum, µ0
µ0 = 4 x 10-7 H/m

RL TIME CONSTANT
Where:
= RL time constant in Seconds (s) (Greek letter Tau)
GENERAL EXPONENTIAL VOLTAGE FORMULA
Where:
v = Instantaneous voltage at time, t, in Volts (V)
VF = Voltage final value in Volts (V)
Vi = Voltage initial value in Volts (V)
INDUCTOR ENERGY STORAGE
Where:
TOTAL INDUCTANCE - SERIES

Where:
LT = Total series inductance in Henries (H)
Ln = Circuit’s last inductor in Henries (H)
TOTAL INDUCTANCE – PARALLEL
Where:
LT = Total parallel inductance in Henries (H)
Ln
= Circuit’s last inductor in Henries (H)
RL CIRCUIT CURRENT INCREASE AND DECREASE
FOR GIVEN NUMBER OF TIME CONSTANTS
# of Time Constants
Approx % of Final Current
Approx % of Initial Charge
1
63
37
2
86
14
3
95
5
4
98
2
5
99
Considered 100%
1

Considered 0%
GENERAL EXPONENTIAL CURRENT FORMULA
Where:
i = Instantaneous current at time, t, in Amperes (A)
IF = Current final value in Amperes (A)
Ii = Current initial value in Amperes (A)
INDUCTIVE REACTANCE
Where:
XL = Inductive reactance in Ohms (Ω)
Note:
= 3.1416 (Greek letter “Pi”)
INDUCTOR REACTIVE POWER
Where:
Pr = Reactive Power in Watts (W)
Vrms = Voltage rms in Volts (V)
Irms = Current rms in Amperes (A)

UNIT 2: RL CIRCUITS
SERIES RL CIRCUIT
IMPEDANCE IN RECTANGULAR FORM
Where:
Z = Impedance in Ohms (Ω)
Note:
Bold letters represent complete phasor quantities.
For example, “
Z” in the formula above
VOLTAGE IN RECTANGULAR FORM
Where:
Vs = Voltage in Volts (V)
VR = Resistor voltage in Volts (V)
VL = Inductor voltage in Volts (V)
INDUCTOR TRUE POWER
Where:
Ptrue = True Power in Watts (W)
RW = Winding resistance in Ohms (Ω)

COIL QUALITY FACTOR
Where:
Q = Coil quality factor (Unitless)
RW = Winding resistance of the coil or the resistance
in series with the coil in Ohms (Ω)
Note:
Circuit Q and the coil Q are the same when the resistance is
only the coil winding resistance
IMPEDANCE IN POLAR FORM
Where:
Note:
= Magnitude
= Phase Angle
VOLTAGE IN POLAR FORM
Where:

VL = Inductor voltage in Volts (V)
LEAD CIRCUIT
ANGLE BETWEEN VOLTAGE IN & OUT
Where:
= Angle between voltage in and out in Degrees (0)
OUTPUT VOLTAGE MAGNITUDE
Where:
Vout = Voltage output in Volts (V)
LAG CIRCUIT
Where:

Where:
Vout = Output voltage in Volts (V)
Vin = Input voltage in Volts (V)
PARALLEL RL CIRCUIT
TOTAL 2-COMPONENT IMPEDANCE
Where:
Z = Total 2-component impedance in Ohms (Ω)
CURRENT IN POLAR FORM
Where:
Itot = Total current in Amperes (A)
IR = Resistor current in Amperes (A)
IL = Inductor current in Amperes (A)
TOTAL ADMITTANCE
Where:

Y = Total admittance in Siemens (S)
BL = Inductive Susceptance in Siemens (S)
Note:
CURRENT IN RECTANGULAR FORM
Where:
PARALLEL TO SERIES FORM CONVERSION
Where:
Req = Resistance in Ohms (Ω)
POWER
RL CIRCUIT REACTIVE POWER
Where:
Pr = Reactive power in Volt-Ampere Reactive (VAR)

UNIT 3: CAPACITORS
CAPACITANCE
Where:
C = Capacitance in Farads (F)
ENERGY STORED IN A CAPACITOR
Where:
DIELECTRIC CONSTANT (RELATIVE PERMITTIVITY)
Where:
= Dielectric constant (Unitless)
(Greek letter Epsilon)
= Absolute permittivity of a material in Farads per
meter (F/m)
= Absolute permittivity of a vacuum in Farads per
meter (F/m)
Note:
= 8.85 x 10-12 F/m

CAPACITANCE
Where:
A = Plate area in Meters squared (m2)
= Dielectric constant (Unitless)
d = Plate separation in Meters (m)
Note:
If d is in mils, 1 mil = 2.54 x 10-5 meters
SERIES CAPACITORS
TOTAL CHARGE
Where:
QT = Total charge in Coulombs (C)
Qn = Circuit’s last capacitor charge in Coulombs (C)
TOTAL CAPACITANCE
Where:
CT = Total series capacitance in Farads (F)
Cn
= Circuit’s last capacitor’s capacitance in
Farads (F)
TOTAL CAPACITANCE - TWO CAPACITORS

Where:
VOLTAGE ACROSS A CAPACITOR
Where:
Vx = Voltage drop in Volts (V)
Cx = Capacitor x’s capacitance in Farads (F)
VT = Total voltage in Volts (V)
TOTAL CAPACITANCE - EQUAL-VALUE CAPACITORS
Where:
n = Number of equal value capacitors (Unitless)
PARALLEL CAPACITORS

TOTAL CHARGE
Where:
QT = Total charge in Coulombs (C)
Qn = Circuit’s last capacitor charge in Coulombs (C)
TOTAL CAPACITANCE - EQUAL-VALUE CAPACITORS
Where:
n = Number of equal value capacitors (Unitless)
CAPACITORS IN DC CIRCUITS
RC TIME CONSTANT
Where:
= Time constant in Seconds (s)
TOTAL CAPACITANCE

Where:
Cn
= Circuit’s last capacitor’s capacitance in
Farads (F)
RC CIRCUIT CURRENT INCREASE AND DECREASE
FOR GIVEN NUMBER OF TIME CONSTANTS
# of Time Constants
Approx % of Final Current
Approx % of Initial Charge
1
63
37
2
86
14
3
95
5
4
98
2
5

99
Considered 100%
1
Considered 0%
GENERAL EXPONENTIAL VOLTAGE FORMULA
Where:
v = Instantaneous voltage at time, t, in Volts (V)
VF = Voltage final value in Volts (V)
Vi = Voltage initial value in Volts (V)
CHARGING TIME TO A SPECIFIED VOLTAGE
Where:
v = Specified voltage level in Volts (V)
VF = Final voltage level in Volts (V)
Note:
Assumes Vi = 0 Volts
GENERAL EXPONENTIAL CURRENT FORMULA
Where:
i = Instantaneous current at time, t, in Amperes (A)
IF = Current final value in Amperes (A)

Ii = Current initial value in Amperes (A)
DISCHARGING TIME TO A SPECIFIED VOLTAGE
Where:
v = Specified voltage level in Volts (V)
Vi = Initial voltage level in Volts (V)
Note:
Assumes VF = 0 Volts
CAPACITORS IN AC CIRCUITS
INSTANTANEOUS CAPACITOR CURRENT
Where:
i = Instantaneous current in Amperes (A)
= Instantaneous rate of change of the voltage
across the capacitor in Volts per second (V/s)
CAPACITOR REACTIVE POWER

Where:
Pr = Reactive Power in Volt-Ampere Reactive (VAR)
Vrms = Voltage rms in Volts (V)
XC = Capacitive reactance in Ohms (Ω)
CAPACITIVE REACTANCE
Where:
Note:
= 3.1416 (Greek letter “Pi”)
SWITCHED-CAPACITORS CIRCUITS
AVERAGE CURRENT

Where:
I1(avg) = Instantaneous current in Amperes (A)
V1 = Voltage 1 in Volts (V)
V2 = Voltage 2 in Volts (V)
T = Period of time in Seconds (s)
UNIT 4: RC CIRCUITS
RC SERIES CIRCUITS
IMPEDANCE IN RECTANGULAR FORM
Where:
OHM’S LAW
Where:
VOLTAGE IN RECTANGULAR FORM
Where:

VC = Capacitor voltage in Volts (V)
LEAD CIRCUIT
Where:
EQUIVALENT RESISTANCE
Where:
R = Equivalent resistance in Ohms (Ω)
T = Period of time in Seconds (s)
IMPEDANCE IN POLAR FORM
Where:

VOLTAGE IN POLAR FORM
Where:
VC = Capacitor voltage in Volts (V)
Where:
LAG CIRCUIT
Where:

RC PARALLEL CIRCUITS
TOTAL 2-COMPONENT IMPEDANCE
Where:
Z = Total 2-component impedance in Ohms (Ω)
OHM’S LAW
Where:
Y = Admittance in Siemens (S)
CURRENT IN RECTANGULAR FORM
Where:
IC = Capacitor current in Amperes (A)
PARALLEL TO SERIES FORM CONVERSION
Where:

Where:
TOTAL ADMITTANCE
Where:
Y = Total admittance in Siemens (S)
BC = Capacitive susceptance in Siemens (S)
Note:
CURRENT IN POLAR FORM
Where:
RC SERIES –PARALLEL CIRCUITS

PHASE ANGLE
Where:
POWER
APPARENT POWER
Where:
Pa = Apparent power in Volt-ampere (VA)
POWER FACTOR
Where:
PF = Power Factor (Unitless)
= Phase angle in Degrees (0)
OSCILLATOR AND FILTER
OSCILLATOR OUTPUT FREQUENCY
Where:
fr = Output frequency in Hertz (Hz)
Note:
= 3.1416
UNIT 5: RLC CIRCUITS AND PASSIVE FILTERS

RLC SERIES CIRCUITS
TOTAL REACTANCE
Where:
Xtot = Total reactance in Ohms (Ω)
TOTAL IMPEDANCE IN POLAR FORM
Where:
Z = Total impedance in Ohms (Ω)
Xtot = Total reactance in Ohms (Ω)
Note:
When XL > XC, the angle is positive
When XC > XL, the angle is negative
TRUE POWER
Where:
Ptrue = True power in Watts (W)
= Phase angle in Degrees (0)

FILTER CUTOFF FREQUENCY
Where:
fc = Cutoff frequency in Hertz (Hz)
Note:
= 3.1416
TOTAL IMPEDANCE IN RECTANGULAR FORM
Where:
Z = Total impedance in Ohms (Ω)
RESONANT FREQUENCY
Where:
fr = Resonant frequency in Hertz (Hz)
Note:
At resonance, XL = XC and the j terms cancel
= 3.1416
RLC PARALLEL CIRCUITS
TOTAL CURRENT
Where:

ICL = Total current into the L and C branches
in Amperes (A)
RLC PARALLEL RESONANCE
RESONANT FREQUENCY - IDEAL
Where:
Note:
At resonance, XL = XC and Zr =
= 3.1416
CURRENT AND PHASE ANGLE

Where:
Zr = Impedance at resonance in Ohms (Ω)
RESONANT FREQUENCY - PRECISE
Where:
Note:
= 3.1416
RLC SERIES – PARALLEL CIRCUITS
SERIES-PARALLEL TO PARALLEL CONVERSION
EQUIVALENT INDUCTANCE
Where:
Leq = Equivalent inductance in Henries (H)

EQUIVALENT PARALLEL RESISTANCE
Where:
Rp(eq) = Equivalent parallel resistance in Ohms (Ω)
NON-IDEAL TANK CIRCUIT
TOTAL IMPEDANCE AT RESONANCE
Where:
ZR = Total impedance in Ohms (Ω)
RW = Resistance in Ohms (Ω)
SPECIAL TOPICS
RESONANT CIRCUIT BANDWIDTH
BANDWIDTH
Where:
BW = Bandwidth in Hertz (Hz)
f2 = Upper critical frequency at Z=0.707·Zmax
in Hertz (Hz)
f1 = Lower critical frequency at Z=0.707·Zmax
in Hertz (Hz)

BANDWIDTH AND QUALTIY FACTOR
Where:
fr = Center (resonant) frequency in Hertz (Hz)
PASSIVE FILTERS
POWER RATIO IN DECIBELS
Where:
dB = Power ratio in decibels (dB)
Pout = Output power in Watts (W)
Pin = Input power in Watts (W)
OVERALL QUALITY FACTOR WITH AN EXTERNAL LOAD
Where:
QO = Overall quality factor (Unitless)
Rp(tot)= Total parallel equivalent resistance in Ohms (Ω)
CENTER (RESONANT) FREQUENCY
Where:
fr = Center (resonant) frequency in Hertz (Hz)
f1 = Lower critical frequency at Z=0.707·Zmax
in Hertz (Hz)

f2 = Upper critical frequency at Z=0.707·Zmax
in Hertz (Hz)
VOLTAGE RATIO IN DECIBELS
Where:
dB = Power ratio in decibels (dB)
Vout = Output voltage in Volts (V)
Vin = Input voltage in Volts (V)
LOW-PASS & HIGH-PASS FILTERS
RC FILTERS
Where:
fC = Filter critical frequency in Hertz (Hz)
Note:

= 3.1416
At fC, Vout = (0.707)·Vin
SERIES RESONANT BAND-PASS FILTER
Where:
f0 = Center frequency in Hertz (Hz)
RL FILTERS
Where:
fc = Filter critical frequency in Hertz (Hz)
Note:
= 3.1416
At fC, Vout = (0.707)·Vin
GENERAL INFORMATION
AREA AND VOLUMES
AREAS

CIRCLE AREA
Where:
A = Circle area in meters squared (m2)
r = Radius in meters (m)
Note:
= 3.1416
RECTANGULAR AND POLAR FORMS
RECTANGULAR FORM
Where:
A = Coordinate value on real axis (Horizontal Plane)

j = j operator
B = Coordinate value on imaginary axis (Vertical Plan)
Note:
“j operator” prefix indicates designated coordinate value is on
imaginary axis.
COMPLEX PLANE AND RECTANGULAR FORM PHASOR
+A
Quadrant 1
Quadrant 3
Quadrant 4
-A
+jB
-jB
(A + jB)
(A - jB)
(-A + jB)
(-A - jB)
Quadrant 2
00/3600
1800
900
2700
POLAR FORM
Where:
C = Phasor magnitude
= Phasor angle relative to the positive real axis

COMPLEX PLANE AND POLAR FORM PHASOR
Real Axis
Quadrant 1
Quadrant 3
Quadrant 4
+j
-j
Length = Magnitude
-
Quadrant 2
+
RECTANGULAR TO POLAR CONVERSION
Where:
j = j operator
Note:
To calculate C:
To calculate in Quadrants 1 and 4 (A is positive):
Use +B for +B values, -B for –B values
To calculate in Quadrants 2 and 3 (A is negative):
Use for +B values

Use for –B values
POLAR TO RECTANGULAR CONVERSION
Where:
j = j operator
Note:
To calculate A:
To calculate B:
Electric Circuits Lab
Capacitors in DC Circuits
I.
Objectives:
After completing this lab experiment, you should be able to:
· Measure the resistance and capacitance.
· Familiarize with Oscilloscope and Function generator.
· Measure the RC time constant using VR and VC.
· Understand the effect of series and parallel capacitors on RC
time constant.
II.
Parts List:
· Resistor (1) 1 kΩ

· Capacitors (2) 0.22 µF
III.
Procedures:
Part I:
1.
Construct the circuit shown in
Figure 1 in Mutism.
Figure 1: Series RC Circuit
2.
Connect Channel A of the oscilloscope across the
voltage source and Channel B across the capacitor.
3.
Set the function generator to
5Vpp; 100 Hz, Square Wave 50% duty cycle with 2.5
DC offset if using a function generator
. If using clock voltage, set it to 5Vpp, 100 Hz. The DC
offset can be modeled by using DC mode on the oscilloscope.
4.
Observe the signals on the scope screen. See
Figure 2(a) below. (Use Volts/Div and Time/DIV
settings to adjust the signal)
Figure 2(a): Voltage across the Voltage Source and the

capacitor
5.
Disable Channel A, by setting it to 0, while observing
Channel B. You should be able to see the waveform as shown
below. Use time base and Channel A scale to adjust the signal.
Figure 2(b): Voltage across the capacitor
6. Change the time base (Sec/Div) until you have a clear
waveform on the scope as shown in
Figure 2(c).
Figure 2(c): Voltage across the capacitor
7.
Calculate the time constant of the RC circuit using the
circuit parameter values.
Record the result in
Table 1 under calculated value.
Calculated value
Measured value using VC
Measured value using VR
220.049us
220.015us
Table 1: Calculated and measured values

8.
Measuring the time constant with VC:
i.
Measure the peak value of the signal, by placing one of
the cursors (T1) at the peak point ___5V______.
ii.
Calculate the 63% of the above value _____3.15 V____.
iii. Place the second cursor (T2) at the step (ii) value above and
T1 at zero just before the capacitor voltage starts rising as
shown in
Figure 3.
iv.
Observe the value of T2-T1 on the scope, which is the
one time constant, as shown below.
v.
Table 1 above under measured value using VC.
Figure 5: Measuring RC time constant using VC
9.
Connect Channel B of the oscilloscope across the
resistor.
10. You should be able to see the waveform as shown below.
(Use Volts/Div and Time/DIV knobs to adjust the signal)
Figure 6(a): Voltage across the resistor

11.
Measuring the time constant with VR:
i.
the cursors (T1) at the peak point ___5 v______.
ii.
Calculate the 37% of the above value ___1.85 V______.
iii. Place the second cursor (T2) at the step (ii) value above.
iv. Observe the T2-T1 value on the scope, which is the one time
constant.
v.
Table 1under measured value using VR.
Figure 6(b): Measuring RC time-constant
using VR
Part II:
12.
Place two capacitors in series as shown in
Figure 7 below.
Figure 7: Series Capacitors
13.
Calculate the total capacitance value and
record the results in
Table 2 below.

Calculated Value
Measured Value
Capacitance
11µF
10.2µF
Table 2: Series Capacitors
14.
Measure the total capacitance value. Use the following
procedure to measure the capacitance in Multisim.
i.
Connect the impedance Meter
(Simulate>>Instruments>>LabView Instruments>>Impedance
Meter) as shown in
Figure 8.
ii.
Measure the capacitive reactance, XC, as shown in
Figure 8.
iii.
Calculate the capacitance using the equation, and
record the value in
Table 2.
Figure 8: Impedance Meter in Multisim
15.
Modify the circuit as shown below, by placing two
0.22µF capacitors in series as in
Figure 8.

Figure 8: RC circuit with two series capacitors
16.
Calculate the new RC time constant using measured
values.
Table 3 below.
Calculated value
114.653 us
17.
resistor
18. Adjust the trigger if needed, and you should be able to see
the waveform as shown in
Figure 9 below.
Figure 9: Voltage Across the Resistor
19.
Repeat step 11.
Record the measured time constant in

Table 3 above.
Part III:
20.
Place two capacitors in parallel as shown in
Figure 10 below. (
Note: The 0.001 Ω resistor is
ONLY required for simulation in Multisim. Without the
resistor, the mathematical model will not converge).
Figure 10: Parallel Capacitors
21.
Table 4 below.
Calculated Value
Measured Value
Capacitance
0.44µF
0.442µF
Table 4: Parallel Capacitors
22.

i.
Meter).
ii.
Measure the capacitive reactance.
iii.
record the value in
Table 4.
23.
Modify the circuit by placing two 0.22µF capacitors in
parallel as in
Figure 11.
Figure 11: RC Circuit with Parallel Capacitors
24.
values.
Table 5 below.
25.
resistor.
26. You should be able to see the waveform as in
Figure 12 below. (Use Volts/Div and Time/DIV knobs
to adjust the signal)
27. Use the cursors on the oscilloscope to

measure the time constant (refer to step 11).
Table 5 below under measured value.
Figure 12: Voltage across the resistor
Calculated value
458.611us
1
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Electric Circuits Lab
Instructor: -----------
Capacitors in DC Circuits
Student Name(s): Click or tap here to enter text.
Click or tap here to enter text.
Honor Pledge:
I pledge to support the Honor System of ECPI. I will refrain
from any form of academic dishonesty or deception, such as
cheating or plagiarism. I am aware that as a member of the
academic community, it is my responsibility to turn in all
suspected violators of the honor code. I understand that any
failure on my part to support the Honor System will be turned
over to a Judicial Review Board for determination. I will report
to the Judicial Review Board hearing if summoned.
Date: 1/1/2018
Contents
Abstract 3
Introduction 3
Procedures 3
Data Presentation & Analysis 4
Calculations 4

Required Screenshots 4
Conclusion 4
References 5
Abstract
(This instruction box is to be deleted before submission of the
Lab report)
What is an Abstract?
This should include a brief description of all parts of the lab.
The abstract should be complete in itself. It should summarize
the entire lab; what you did, why you did it, the results, and
your conclusion. Think of it as a summary to include all work
done. It needs to be succinct yet detailed enough for a person to
know what this report deals with in its entirety.
Objectives of Week 3 Lab 1:
· Measure the resistance and capacitance.
· Familiarize with Oscilloscope and Function generator.
· Measure the RC time constant using VR and VC.
· Understand the effect of series and parallel capacitors on RC
time constant.
Introduction
Lab report)
What is an Introduction?
In your own words, explain the reason for performing the
experiment and give a concise summary of the theory involved,
including any mathematical detail relevant to later discussion in
the report. State the objectives of the lab as well as the overall
background of the relevant topic.

Address the following items in your Introduction:
· What is the time constant for an RC circuit and what is its
significance?
· How do capacitors combine in series? (Give formula)
· How do capacitors combine in parallel? (Give formula)
· What is capacitive reactance? (Give formula)
Procedures
Part I:
1.
Construct the circuit shown in
Figure 1 in Mutism.
Figure 1: Series RC Circuit
2.
voltage source and Channel B across the capacitor.
3.
Set the function generator to
5Vpp; 100 Hz, Square Wave 50% duty cycle with 2.5
DC offset if using a function generator
. If using clock voltage, set it to 5Vpp, 100 Hz. The DC
offset can be modeled by using DC mode on the oscilloscope.
4.
Observe the signals on the scope screen. See
Figure 2(a) below. (Use Volts/Div and Time/DIV
settings to adjust the signal)

Figure 2(a): Voltage across the Voltage Source and the
capacitor
5.
Disable Channel A, by setting it to 0, while observing
Channel B. You should be able to see the waveform as shown
below. Use time base and Channel A scale to adjust the signal.
Figure 2(b): Voltage across the capacitor
6. Change the time base (Sec/Div) until you have a clear
waveform on the scope as shown in
Figure 2(c).
Figure 2(c): Voltage across the capacitor
7.
Calculate the time constant of the RC circuit using the
circuit parameter values.
Table 1 under calculated value.
8.
Measuring the time constant with VC:
i.
the cursors (T1) at the peak point ____5V_____.
ii.
Calculate the 63% of the above value __3.15V_______.

iii. Place the second cursor (T2) at the step (ii) value above and
T1 at zero just before the capacitor voltage starts rising as
shown in
Figure 3.
iv.
Observe the value of T2-T1 on the scope, which is the
one time constant, as shown below.
v.
Table 1 above under measured value using VC.
Figure 5: Measuring RC time constant using VC
9.
Connect Channel B of the oscilloscope across the
resistor.
10. You should be able to see the waveform as shown below.
(Use Volts/Div and Time/DIV knobs to adjust the signal)
Figure 6(a): Voltage across the resistor
11.
Measuring the time constant with VR:
·
the cursors (T1) at the peak point ____5V_____.
·

Calculate the 37% of the above value ____1.85V_____.
· Place the second cursor (T2) at the step (ii) value above.
· Observe the T2-T1 value on the scope, which is the one time
constant.
·
Table 1 above under measured value using VR.
Figure 6(b): Measuring RC time-constant
using VR
Part II:
12.
Place two capacitors in series as shown in
Figure 7 below.
Figure 7: Series Capacitors
13.
Table 2.
14.
·
Meter) as shown in
Figure 8.

·
Measure the capacitive reactance, XC, as shown in
Figure 8.
·
record the value in
Table 2.
Figure 8: Impedance Meter in Multisim
15.
Modify the circuit as shown below, by placing two
0.22µF capacitors in series as in
Figure 8.
Figure 8: RC circuit with two series capacitors
16.
values.
Table 3.
17.
resistor
18. Adjust the trigger if needed, and you should be able to see
the waveform as shown in
Figure 9 below.

Figure 9: Voltage Across the Resistor
19.
Repeat step 11.
Record the measured time constant in
Table 3.
Part III:
20.
Place two capacitors in parallel as shown in
Figure 10 below. (
Note: The 0.001 Ω resistor is
ONLY required for simulation in Multisim. Without the
resistor, the mathematical model will not converge).
Figure 10: Parallel Capacitors
21.
Table 4 below.
22.
·

Meter).
·
Measure the capacitive reactance.
·
record the value in
Table 4.
23.
Modify the circuit by placing two 0.22µF capacitors in
parallel as in
Figure 11.
Figure 11: RC Circuit with Parallel Capacitors
24.
values.
Table 5.
25.
resistor.
26. You should be able to see the waveform as in
Figure 12 below. (Use Volts/Div and Time/DIV knobs
to adjust the signal)
27. Use the cursors on the oscilloscope to
measure the time constant (refer to step 11).
Table 5 under measured value.

Figure 12: Voltage across the resistorData Presentation &
Analysis
Calculated value
Measured value using VC
220.049us
220.015us
Table 1: Calculated and measured time constant values
Calculated Value
Measured Value
Capacitance
11µF
10.2µF
Table 2: Series Capacitors
Calculated value
Time consta
114.643us
Calculated value

Measured value
Capacitance
0.44µF
0.442µF
Table 4: Parallel Capacitors
Calculated value
Calculations
Lab report)
Show all of your calculations in this section.
Part 2 step 13: CT =
Lab report)
Place screenshots of measurements in this section. You may
change the names of the figures as the ones provided show the
required content.

Figure 13: Screenshot of Waveforms Part 1 Step 8
Figure 15: Screenshot of Impedance Meter Part 2 Step 14
Figure 17: Screenshot of Impedance Meter Part 3 Step 22
Figure 18: Screenshot of Waveforms Part 3 Step 27Conclusion
Lab report)
What is a Conclusion?
This section should reflect your understanding of the
experiment conducted. Important points to include are a brief
discussion of your results, and an interpretation of the actual
experimental results as they apply to the objectives of the
experiment set out in the introduction should be given. Also,
discuss any problems encountered and how they were resolved.
Address the following in your conclusions:
· Did your measured results match your calculated values? If
not, why not?
· What happened to the overall capacitance when you went from
one series capacitor to two? (Did capacitance increase or
decrease?)
· What happened to the overall capacitive reactance when you
went from one series capacitor to two? (Did the capacitive
reactance increase or decrease?)
· What happened to the time constant when you went from one
series capacitor to two? (Did the time constant increase or
decrease?)
· What happened to the overall capacitance when you went from
one capacitor to two parallel capacitors? (Did the capacitance
increase or decrease?)
· What happened to the overall capacitive reactance when you

went from one capacitor to two parallel capacitors? (Did the
capacitive reactance increase or decrease?)
· What happened to the time constant when you went from one
capacitor to two parallel capacitors? (Did the time constant
increase or decrease?)
References
Floyd, T. L., & Buchla, D. M. (2019).
Principles of Electric Circuits (10th Edition). Pearson
Education (US).
https://bookshelf.vitalsource.com/books/9780134880068
(2017) National Instruments Multisim (V 14.1) [Windows].
Retrieved from http://www.ni.com/multisim/
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