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Chapter 2 Summary
Electric Circuits and Components
dq
I ( t ) = -----dt
current (A):
V = IR
ohm's law (V):
R = ab ´ 10c ± tolerance (%)
resistor value (W):
a, b, and c Bands
tol Band
Color
Value
Color
Value
Black
0
Gold
±5%
Brown
1
Silver
±10%
Red
2
Nothing
±20%
Orange
3
Yellow
4
Green
5
Blue
6
Violet
7
Gray
8
White
9
t
capacitor (F):
1
V ( t ) = ---C
dV
I ( t ) = C -----dt
Q(t)
ò I ( t )dt = ---------C
0
t
inductor (H):
dI
V ( t ) = L ----dt
1
I ( t ) = --L
ò V ( t ) dt
0
N
Kirchoff's Voltage Law (KVL):
å Vi
= 0
i=1
N
Kirchoff’s Current Law (KCL):
å Ii
= 0
i=1
series resistors:
R eq = R 1 + R 2
series capacitors:
C1 C2
C eq = ----------------C1 + C2
series inductors:
L eq = L 1 + L 2
series resistor voltage division:
R1
- Vs ,
V R1 = ---------------R1 + R 2
parallel resistors
1
1
1
------- = ----- + ----R 1 R2
R eq
R2
- Vs
V R2 = ---------------R 1 + R2
R1 R2
R eq = ---------------R1 + R2
parallel capacitors:
C eq = C 1 + C 2
parallel inductors:
L1L2
L eq = ---------------L1 + L2
parallel resistor current division:
R2
- I,
I 1 = ---------------R 1 + R2
R1
-I
I 2 = ---------------R 1 + R2
ideal voltage source: zero output resistance, can supply infinite current.
ideal current source: infinite output resistance, can supply infinite voltage.
ideal voltmeter: infinite input resistance, draws no current.
ideal ammeter: zero input resistance, no voltage drop.
V ( t ) = V m sin ( wt + f )
ac signal:
1
w
f = --- = -----T
2p
frequency (Hz):
phasor:
V = Vm e
j ( wt + f )
= V m á fñ = V m [ cos ( wt + f ) + j sin ( wt + f )]
phasor relationships:
r =
2
2
x +y
–1 y
f = tan æ --ö
è xø
r 1 á f 1ñ × r 2 á f 2ñ = r 1 × r 2 á f 1 + f 2ñ
r 1 á f 1ñ ¤ r 2 á f 2ñ = r 1 ¤ r 2 á f 1 – f 2ñ
ac Ohm’s Law with impedance:
V = ZI
resistor impedance:
ZR = R
inductor impedance:
Z L = jwL = wL á 90°ñ
capacitor impedance:
1
1
–j
Z C = ---------- = -------- = -------- á – 90°ñ
wC
jwC
wC
power:
dq
dW
P = -------- = V ------ = VI
dt
dt
dc resistive power:
P = VI = I 2 R = V 2 ¤ R
T
rms:
I rms =
Im
1
--- I 2 dt = -----T
2
ò
0
ac resistive power:
transformer:
T
V rms =
V
1
--- V 2 dt = ------mT
2
ò
0
P avg = V rms I rms = RI2rms = V 2rms ¤ R
N
V S = -----S- V P
NP
N
I S = -----P- I P
NS