DC Circuits
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This activity is based on the following concepts:
The power delivered by an EMF source is given by
i
ε
.
The power dissipated by a
single
resistor is given by
iV
, where
V
is the potential drop
across
just
that
resistor.
For resistances in series: the net resistance is equal to the sum of all resistances in series:
For resistances in
parallel: the net reciprocal resistance is equal to the sum of all
reciprocal resistances in parallel:
The loop rule:
o
Follow a closed loop around any circuit; the sum of
all
the changes in potential that
you encounter must
equal
ze
ro.
The junction rule:
o
The algebraic sum of currents at a junction in a circuit must equal zero.
Exercise 1
The circuits shown below are all constructed using identical bulbs of resistance
R
and ideal
batteries of EMF
ε
. Assume for simplicity that the resistance of a bulb does not depend on the
temperature of its filament (in reality, of course, it does depend upon this).
Q1.
Rank the circuits in order of increasing power supplied by th
e battery
, defending your
ranking with physical reasoning or a calculation
.
(
Hint
: the battery provides exactly the same
emf
ε
in each of the four circuits, but the current provided by the battery in each case is
dependent upon the total resistance in the
circuit.)
+
−
+
−
+
−
+
−
A
B
C
D
X
X
X
X
Q2.
In each of the four circuits, a bulb has been labeled '
X
'. Rank the circuits above according to
how bright bulb '
X
' is, in order of increasing brightness. (Assume that the brightness of the bulb
is directly proportional to the
power it diss
i
pates.) Again,
defend your ranking based on a clear
statement of your physical reasoning or a calculation which supports your claim.
Exercise 2
Consider the circuit shown below. Use the junction and loop rules to
set up a system of equations
that would allow you to
determine the currents through the three resistors.
Be sure to label the
figure with your expectation as to which
direction
each current
flows through the resistors
.
(
Optional
: if time permits, solve you
r system of equations for the current through each resistor.)
+
−
+
−
+
−
20 Ω
㤠9
10 Ω
㤠9
20 Ω
㤠9
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