D
IRECT
C
URRENT
C
IRCUITS
PART
2
26.15.
IDENTIFY:
In both circuits, with and without
R
4
, replace series and parallel combinations of resistors by their
equivalents. Calculate the currents and voltages in the equivalent circuit and infer from this the currents and
voltages in the original circuit. Use
to calculate the power dissipated in each bulb.
(a) SET UP:
The circuit is sketched in Figure 26.13a.
EXECUTE:
are in
parallel, so their equivalent resistance
is given by
Figure 26.13a
The equivalent circuit is drawn in Figure 26.13b.
Figure 26.13b
Then
For resistors in parallel the voltages are equal and are the same as the voltage across the equivalent resistor, so
EVALUATE:
Note that
which is
For resistors in parallel the currents add and their sum
is the current through the equivalent resistor.
(b) SET UP:
EXECUTE:
which rounds to 1.12 W.
glows brightest.
EVALUATE:
Note that
This equals
the power
dissipated in the equivalent resistor.
(c) SET UP:
With
removed the circuit becomes the circuit in Figure 26.13c.
26
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View Full DocumentEXECUTE:
are in parallel and
their equivalent resistance
is given by
and
Figure 26.13c
The equivalent circuit is shown in Figure 26.13d.
Figure 26.13d
(d) SET UP:
EXECUTE:
(e) EVALUATE:
When
R
4
is removed,
P
1
decreases and
P
2
and
P
3
increase. Bulb
R
1
glows less brightly and bulbs
R
2
and
R
3
glow more brightly. When
R
4
is removed the equivalent resistance of the circuit increases and the current
through
R
1
decreases. But in the parallel combination this current divides into two equal currents rather than three,
so the currents through
R
2
and
R
3
increase. Can also see this by noting that with
R
4
removed and less current
through
R
1
the voltage drop across
R
1
is less so the voltage drop across
R
2
and across
R
3
must become larger.
26.26.
IDENTIFY:
Apply the loop rule and junction rule.
SET UP:
The circuit diagram is given in Figure 26.22. The junction rule has been used to find the magnitude and
direction of the current in the middle branch of the circuit. There are no remaining unknown currents.
EXECUTE:
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 Spring '10
 Hirsch
 Resistor, Electrical resistance, Series and parallel circuits, loop rule

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