1
Lehigh University
Physics 21, Spring 2008
March 3, 2008
HW15 Solutions
151.
(HRW 3064)
A coil with an inductance of 2.7 H and a resistance of 8.5
Ω
is
suddenly connected to an ideal battery with
ε
= 100 V. At 0.086 s after the connection is
made, what is the rate at which
(a)
energy is being stored in the magnetic field,
(b)
thermal energy is appearing in the resistance, and
(c)
energy is being delivered by the
battery?
Solution:
64. (a) From Eq. 3049 and Eq. 3041, the rate at which the energy is being stored in the
inductor is
()
2
1
2
2
1
11
.
L
LL
L
tt
t
t
B
L
dL
i
dU
di
Li
L
e
e
e
e
dt
dt
dt
R
R
R
τ
ττ
εε
ε
−−
−
−
⎛⎞
==
=
−
=
−
⎜⎟
⎝⎠
Now,
L
= L
/
R
= 2.0 H/10
Ω
= 0.20 s
and
= 100 V, so the above expression yields
dU
B
/
dt
= 2.4
×
10
2
W when
t
= 0.10 s.
(b) From Eq. 2622 and Eq. 3041, the rate at which the resistor is generating thermal
energy is
Pi
R
R
eR
R
e
thermal
−
=
−
2
2
2
2
2
2
chch
.
At
t
= 0.10 s, this yields
P
thermal
= 1.5
×
10
2
W.
(c) By energy conservation, the rate of energy being supplied to the circuit by the battery
is
PP
dU
dt
B
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 Spring '08
 Kim
 Inductance, Resistance, Energy, Magnetic Field, Fundamental physics concepts, Energy density, HRW, DT DT DT

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