The_Cambridge_Handbook_of_Physics_Formulas

7.6 LCR circuits
147
7.6 LCR circuits
LCR definitions
Current
I = dQ
dt
(7.139)
I
Q
current
charge
Ohm’s law V = IR (7.140)
Ohm’s law (field
form)
Resistivity
Capacitance
Current through
capacitor
J = σE (7.141)
ρ = 1 σ = RA
l
C = Q V
I = C dV
dt
(7.142)
(7.143)
(7.144)
R
resistance
V potential difference
over R
I current through R
J current density
E electric field
σ conductivity
ρ resistivity
A area of face (I is
normal to face)
l length ✍
C capacitance
V potential difference
across C
I
t
current through C
time
✼
✴ l
A
Self-inductance
Voltage across
inductor
Mutual
inductance
L = Φ I
V = −L dI
dt
(7.145)
(7.146)
L 12 = Φ 1
I 2
= L 21 (7.147)
Φ
I
V
total linked flux
current through
inductor
potential difference
over L
Φ 1 total flux from loop 2
linkedbyloop1
L 12 mutual inductance
I 2 current through loop 2
7
Coefficient of
coupling
|L 12 | = k √ L 1 L 2 (7.148) k coupling coefficient
between L 1 and L 2
(≤ 1)
Linked magnetic
flux through a coil
Φ=Nφ (7.149)
Φ
N
φ
linked flux
number of turns
around φ
flux through area of
turns