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Section:
QUIZ #3
Electric Currents and Resistors
Physics 222, Fall 2011
Sep. 13, 2011
Version A
Two resistors
R
and 4
R
can be connected in parallel with an ideal battery (no internal resistance) or
in series with the same battery. What is the ratio of the total power dissipation in the series circuit
to the total power dissipation in the parallel circuit?
Solution
The power dissipation in the circuit can be calculated by using one of the following three equations:
P
tot
=
V
2
R
eq
,
=
V I
tot
,
=
I
2
tot
R
eq
,
where
V
is the voltage of the battery. Since we are comparing between two situations where the total
voltage is the same, the first equation is most suitable for the task. The second and third equations
require calculating
R
eq
anyway to get current, so they involve an unnecessary step. We now calculate
the total resistance for each of the two connections:
Parallel:
R
parallel
=
1
R
+
1
4
R

1
=
4
5
R
Series:
R
series
=
R
+ 4
R
= 5
R.
Then the ratio between the power dissipation in series,
P
series
, and the power dissipation in parallel,
P
parallel
, is:
P
series
P
parallel
=
V
2
/R
series
V
2
/R
parallel
=
R
parallel
R
series
=
4
25
.
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 Fall '09
 MEYER
 Resistor, Electrical resistance, Series and parallel circuits, Rseries

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