Originally published on Yahoo Voices
Contents
Contents
DC Circuit containing one resistor (Figure One)
Rules of Series Circuits
DC Series Circuit containing two resistors R1 and R2 (Figure One)
Rules of Parallel Circuits
DC Parallel Circuit containing two resistors R1 and R2 (Figure One)
AC Series Circuit containing R, C and L (Figure Two)
AC Parallel Circuit containing R and L (Figure Two)
AC Parallel Circuit containing R and C (Figure Two)
AC Parallel Circuit containing L and C (Figure Two)
AC Parallel Circuit containing R, L and C (Figure Two)
AC Power
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DC Circuit containing one resistor (Figure One)
E: electromotive force - Unit of measurement: volts
I: current - Unit of measurement: amperes
R: resistance - Unit of measurement: ohms
P: power - Unit of measurement: watts
A^2 means A squared.
A*(1/2) means square root of A
E = I * R
R = E/I
I = E/R
P = E*I = (I*R) * I = (I^2) * R
E = P/I = (I^2) * R/I = I * R
I = E/P
Rules of Series Circuits
Total voltage = sum of voltage drops
Total current = current through each component
Total Resistance = sum of resistances
DC Series Circuit containing two resistors R1 and R2 (Figure One)
R1: Resistor
R2: Resistor
Vr1: voltage drop across R1
Vr2: voltage drop across R2
Rt: total resistance
E = I * R1 + I * R2
I = same through each component
I = E/(R1 + R2)
Vr1 = I * R1
R1 = Vr1/I
I = Vr1/R
Vr2 = I * R2
R1 = Vr2/I
I = Vr2/R
E = Vr1 + Vr2
Rt = R1 + R2
P = E * I
Rules of Parallel Circuits
Voltage = same across each branch
Current = sum of currents through each branch
Resistance = less than least resistance
DC Parallel Circuit containing two resistors R1 and R2 (Figure One)
I = I*R1 + I*R2
E = same through each branch
E = Vr1 = Vr2
1/Rt = 1/R1 + 1/R2
Rt = R1 * R2/(R1 + R2)
P = E * I
Rules of Series Circuits
Total voltage = sum of voltage drops
Total current = current through each component
Total Resistance = sum of resistances
AC Series Circuit containing R, C and L (Figure Two)
L: Inductor - Unit of Measurement: Henries
C: Capacitor - Unit of Measurement: Farads
XL: Inductive Reactance - Unit of Measurement: Ohms
XC: Capacitive Reactance - Unit of Measurement: Ohms
Z: Impedance - Unit of measurement: Ohms
o: angle - Unit of Measurement: Degrees
X: algebraic sum of XC and XL
j: (-1)^(1/2)
XL = 2 * pi * F * L
XC = 1/(2 * pi * F * C)
Z = R + j*XL - j*XC
Z = R^2 + (XL - XC)^2
Z^2 = R^2 + X^2
Z = Z * (cos o) + j*Z * (sin o)
I = E/Z = same through each component
E = I * (R^2 + (XL - XC)^2 )^(1/2)
angle o = arctan (X/R)
Rules of Parallel Circuits
Voltage = same across each branch
Current = sum of currents through each branch
Resistance = less than least resistance
AC Parallel Circuit containing R and L (Figure Two)
1/Z = 1/R + 1/( j*XL)
I = sum of currents through each branch
I = (I * cos o) + j * (I * sin o)
E = same through each branch
E = I*Z
angle o = arctan (XL/R)
AC Parallel Circuit containing R and C (Figure Two)
Ir: current through R
Ixc: current through XC
1/Z = 1/R + 1/(1/( j*XC))
I = sum of currents through each branch
Ir = E/R
Ixc = E/(- j*XC)
I = Ir - j*Ixc
I = I * cos o - j * I * sin o
E = same through each branch
E = I*Z
angle o = arctan (-XC/R)
AC Parallel Circuit containing L and C (Figure Two)
IXL: current through XL
IXC: current through XC
1/Z = 1/(j*XL) + 1/(1/(j*XC))
I = sum of currents through each branch
IXL = E/(j*XL)
IXC = E/(j*XC)
I = j*IXL - j*IXC
E = same through each branch
E = I*Z
If XL > XC then
angle o = 90 degrees
If Xc > XL then
angle o = -90 degrees
AC Parallel Circuit containing R, L and C (Figure Two)
1/Z = 1/R + 1/(j*XL) + 1/(1/(j*XC))
E = same through each branch
E = I*Z
I equals sum of curents through each branch
I = IR + jIX
IX = I * j*(IXL - IXC)
If XL > XC then
0 < angle o <= 90
If XL < XC then
-90 <= angle o < 0
If XL = XC then
Angle o = 0 degrees
AC Power
AP = Apparent Power
RP = Reactive Power
TP = True Power
PF = Power Factor
TP = V * I * cos o = I^2 * R
RP = V * I * sine o = I^2 * X
AP = V * I = V * I * cos o + j * V * I * sine o
(AP)^2 = (TP)^2 + (RP)^2
PF = cos o = TP/AP
Figure One
Figure Two
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