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14 Electromagnetism II
Solution i =
ξ
R
1 − e
−
Rt
L
(14.6)
Inductive time constant
τ L = L/R
(14.7)
Differential equation L
di
dt
+ iR = 0 (discharging process)
(14.8)
Solution i =
ξ
R
e
−Rt/L
(14.9)
C–R Circuit
Ri + q/c = ξ (charging)
(14.10)
q = q 0 (1 − e
−t/RC
)
(14.11)
Capacitive Time Constant
τ = RC
(14.12)
Ri + q/C = 0 (discharging)
(14.13)
q = q 0 e
−t/RC
(14.14)
Inductors in Series
L eq = L 1 + L 2 + 2M (coil currents in the same sense)
(14.15)
L eq = L 1 + L 2 − 2M (coil currents in the opposite sense)
(14.16)
where M is the mutual inductance
L eq = L 1 + L 2 (inductors well separated)
(14.17)
Inductors in Parallel
L eq = L 1 L 2 /(L 1 + L 2 )
(14.18)
M = (L 1 L 2 )
1/2 (inductors are closely placed)
(14.19)
The Alternating Current (AC)
The effective or root-mean-square value:
I e = I 0 /
√
2
(14.20)
where I 0 is the peak current
14 Electromagnetism II
Solution i =
ξ
R
1 − e
−
Rt
L
(14.6)
Inductive time constant
τ L = L/R
(14.7)
Differential equation L
di
dt
+ iR = 0 (discharging process)
(14.8)
Solution i =
ξ
R
e
−Rt/L
(14.9)
C–R Circuit
Ri + q/c = ξ (charging)
(14.10)
q = q 0 (1 − e
−t/RC
)
(14.11)
Capacitive Time Constant
τ = RC
(14.12)
Ri + q/C = 0 (discharging)
(14.13)
q = q 0 e
−t/RC
(14.14)
Inductors in Series
L eq = L 1 + L 2 + 2M (coil currents in the same sense)
(14.15)
L eq = L 1 + L 2 − 2M (coil currents in the opposite sense)
(14.16)
where M is the mutual inductance
L eq = L 1 + L 2 (inductors well separated)
(14.17)
Inductors in Parallel
L eq = L 1 L 2 /(L 1 + L 2 )
(14.18)
M = (L 1 L 2 )
1/2 (inductors are closely placed)
(14.19)
The Alternating Current (AC)
The effective or root-mean-square value:
I e = I 0 /
√
2
(14.20)
where I 0 is the peak current