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59. (a) If the battery is applied at time
t
= 0 the current is given by
i
=
E
R
³
1
−
e
−
t/τ
L
´
,
where
E
is the emf of the battery,
R
is the resistance, and
τ
L
is the inductive time constant (
L/R
).
This leads to
e
−
t/τ
L
=1
−
iR
E
=
⇒−
t
τ
L
=ln
µ
1
−
iR
E
¶
.
Since
ln
µ
1
−
iR
E
¶
=ln
·
1
−
(2
.
00
×
10
−
3
A)(10
.
0
×
10
3
Ω)
50
.
0V
¸
=
−
0
.
5108
,
the inductive time constant is
τ
L
=
t/
0
.
5108 = (5
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 Fall '08
 SPRUNGER
 Physics, Current, Resistance

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