261
D
IRECT
C
URRENT
C
IRCUITS
These solutions sometimes use Epsilon to denote the EMF of a battery (the curly, script E in the book). Sometimes it
looks like
Ε
,
sometimes
ε
,
so
WATCH OUT.
26.55.
I
DENTIFY
:
We need to do series/parallel reduction to solve this circuit.
S
ET
U
P
:
P
=
ε
2
R
, where
R
is the equivalent resistance of the network. For resistors in series,
R
s
= R
1
+
R
2
, and
for resistors in parallel 1/
R
p
= 1/
R
1
+ 1/
R
2
.
E
XECUTE
:
R
=
ε
2
P
=
(48.0 V)
2
295 W
=
7.810
Ω
.
R
12
=
R
1
+
R
2
=
8.00
Ω
.
R
=
R
123
+
R
4
.
R
123
=
R
−
R
4
=
7.810
Ω −
3.00
Ω
=
4.810
Ω
.
1
R
12
+
1
R
3
=
1
R
123
.
1
R
3
=
1
R
123
−
1
R
12
=
R
12
−
R
123
R
123
R
12
.
R
3
=
R
123
R
12
R
12
−
R
123
=
(4.810
Ω
)(8.00
Ω
)
8.00
Ω −
4.810
Ω
=
12.1
Ω
.
E
VALUATE
:
The resistance
R
3
is greater than
R
, since the equivalent parallel resistance is less than any of the
resistors in parallel.
26.59.
I
DENTIFY
:
The terminal voltage of the battery depends on the current through it and therefore on the equivalent
resistance connected to it. The power delivered to each bulb is
, where
I
is the current through it.
S
ET
U
P
:
The terminal voltage of the source is
.
E
XECUTE
:
(a)
The equivalent resistance of the two bulbs is
This equivalent resistance is in series with the
internal resistance of the source, so the current through the battery is
and the
current through each bulb is 2.2 A. The voltage applied to each bulb is
.
Therefore,
.
(b)
If one bulb burns out, then
. The current through the remaining bulb is
2.9 A, and
. The remaining bulb is brighter than before, because it is
consuming more power.
E
VALUATE
:
In Example 26.2 the internal resistance of the source is negligible and the brightness of the
remaining bulb doesn’t change when one burns out.
26.63.
I
DENTIFY
:
Apply the junction rule to express the currents through the
resistors in terms of
Apply the loop rule to three loops to get three equations in the three unknown currents.
S
ET
U
P
:
The circuit is sketched in Figure 26.61.
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 Spring '10
 Hirsch
 Energy, Resistor, Electrical resistance, Series and parallel circuits

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