fundamentals of engineering supplied-reference handbook - Ventech!

Resistors in Series and Parallel
For series connections, the current in all resistors is the same
and the equivalent resistance for n resistors in series is
i sc
RS = R1 + R2 + … + Rn
For parallel connections of resistors, the voltage drop across
each resistor is the same and the equivalent resistance for n
resistors in parallel is
RP = 1/(1/R1 + 1/R2 + … + 1/Rn)
For two resistors R1 and R2 in parallel
R
P
RR 1 2
=
R + R
SOURCES
AND
RESISTORS
1 2
Power Absorbed by a Resistive Element
2
V 2
P = VI = = I R
R
Kirchhoff's Laws
Kirchhoff's voltage law for a closed path is expressed by
Σ Vrises = Σ Vdrops
Kirchhoff's current law for a closed surface is
Σ Iin = Σ Iout
SOURCE EQUIVALENTS
For an arbitrary circuit
The Thévenin equivalent is
V oc
R eq
R
eq
a
b
a
b
a
b
R eq
Voc i sc
The open circuit voltage Voc is Va – Vb, and the short circuit
current is isc from a to b.
The Norton equivalent circuit is
where isc and Req are defined above.
A load resistor RL connected across terminals a and b will
draw maximum power when RL = Req.
168
i (t)
c
C
ELECTRICAL AND COMPUTER ENGINEERING (continued)
CAPACITORS AND INDUCTORS
v (t)
c
i (t)
L
L
v (t)
L
The charge qC (t) and voltage vC (t) relationship for a
capacitor C in farads is
C = qC (t)/vC (t) or qC (t) = CvC (t)
A parallel plate capacitor of area A with plates separated a
distance d by an insulator with a permittivity ε has a
capacitance
A
C
d
ε
=
The current-voltage relationships for a capacitor are
1 t
vC
() t = vC
( 0 ) + ∫iC
() τ dτ
C 0
and iC (t) = C (dvC /dt)
The energy stored in a capacitor is expressed in joules and
given by
Energy = CvC 2 /2 = qC 2 /2C = qCvC /2
The inductance L of a coil with N turns is
L = Nφ/iL
and using Faraday's law, the voltage-current relations for an
inductor are
vL(t) = L (diL /dt)
1 t
iL
() t = iL
( 0 ) + ∫ vL
() τ dτ
, where
L
0
vL = inductor voltage,
L = inductance (henrys), and
i = inductor current (amperes).
The energy stored in an inductor is expressed in joules and
given by
Energy = LiL 2 /2
Capacitors and Inductors in Parallel and Series
Capacitors in Parallel
CP = C1 + C2 + … + Cn
Capacitors in Series
1
CS
=
1 C + 1 C + … + 1 C
1 2
Inductors in Parallel
1
LP
=
1 L + 1 L + … + 1 L
Inductors in Series
1 2
LS = L1 + L2 + … + Ln
n
n