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Induced Voltages and Inductance
191
20.44
The current in the
RL
circuit at time
t
is
(
1
t
Ie
R
)
τ
ε
−
=−
. The potential difference across
the resistor is
( )
1
t
R
VR
I
e
−
∆== −
, and from Kirchhoff’s loop rule, the potential
difference across the inductor is
( )
11
tt
LR
VV
ee
εε
−−
∆=−
∆=
=
(a) At
0
t
=
,
( )
()
0
1
R
Ve
0
−
− = −=
(b) At
t
=
,
( )
( )
1
1
6.0 V
1
0.368
3.8 V
R
−
− =
−
=
(c) At
0
t
=
,
0
6.0 V
L
−
==
(d) At
t
=
,
1
6.0 V
0.368
2.2 V
L
−
=
=
20.45
From
( )
max
1
t
e
II
−
,
max
1
t
I
e
I
−
If
max
0.900
I
I
=
at
, then
3.00 s
t
=
3.00 s
e
−
0.100
=
or
3.00 s
1.30 s
ln 0.100
−
Since the time constant of an
RL
circuit is
=
, the resistance is
2.50 H
1.9
1.30 s
=
2

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