Induced Voltages and Inductance
191
20.44
The current in the
RL
circuit at time
t
is
(
1
t
I
e
R
)
τ
ε
−
=
−
. The potential difference across
the resistor is
(
)
1
t
R
V
RI
e
τ
ε
−
∆
=
=
−
, and from Kirchhoff’s loop rule, the potential
difference across the inductor is
(
)
1
1
t
t
L
R
V
V
e
e
τ
τ
ε
ε
ε
−
−
∆
=
− ∆
=
−
−
=
(a) At
0
t
=
,
(
)
(
)
0
1
1
1
R
V
e
0
ε
ε
−
−
=
−
=
∆
=
(b) At
t
τ
=
,
(
)
(
)(
)
1
1
6.0 V
1
0.368
3.8 V
R
V
e
ε
−
−
=
−
=
∆
=
(c)
At
0
t
=
,
0
6.0 V
L
V
e
ε
ε
−
=
=
∆
=
(d) At
t
τ
=
,
(
)(
)
1
6.0 V
0.368
2.2 V
L
V
e
ε
−
=
=
∆
=
20.45
From
(
)
max
1
t
e
I
I
τ
−
=
−
,
max
1
t
I
e
I
τ
−
=
−
If
max
0.900
I
I
=
at
, then
3.00 s
t
=
3.00 s
e
τ
−
0.100
=
or
(
)
3.00 s
1.30 s
ln 0.100
τ
−
=
=
Since the time constant of an
RL

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