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PHYS202SP2008
Week 7  part 2
Due at 6:00pm on Saturday, May 17, 2008
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Kirchhoff's Rules and Applying Them
Learning Goal:
To understand the origins of both of Kirchhoff's rules and how to use them to solve a circuit
problem.
This problem introduces Kirchhoff's two rules for circuits:
•
Kirchhoff's loop rule
: The sum of the voltage changes across the circuit elements forming any closed
loop is zero.
•
Kirchhoff's junction rule
: The algebraic sum of the currents into (or out of) any junction in the circuit is
zero.
The figure
shows a circuit that illustrates the concept
of
loops
, which are colored red and labeled loop 1 and loop 2. Loop 1 is the loop around the entire circuit,
whereas loop 2 is the smaller loop on the right. To apply the loop rule you would add the voltage changes of all
circuit elements around the chosen loop. The figure contains two junctions (where three or more wires meet)
they are at the ends of the resistor labeled
. The battery supplies a constant voltage
, and the resistors are
labeled with their resistances. The ammeters are ideal meters that read
and
respectively.
The direction of each loop and the direction of each current arrow that you draw on your own circuits are
arbitrary. Just assign voltage drops consistently and sum both voltage drops and currents algebraically and you
will get correct equations. If the actual current is in the opposite direction from your current arrow, your answer
for that current will be negative. The direction of any loop is even less imporant: The equation obtained from a
counterclockwise loop is the same as that from a clockwise loop except for a negative sign in front of every term
(i.e., an inconsequential change in overall sign of the equation because it equals zero).
Part A
The junction rule describes the conservation of which quantity? Note that this rule applies only to circuits that
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View Full DocumentKirchhoff's Rules and Applying Them
Part A
are in a steady state.
Hint A.1
At the junction
Think of the analogy with water flow. If a certain current of water comes to a split in the pipe, what can you
say (mathematically) about the sum of the three water currents at this junction? If this were not true, water
would accumulate at the junction.
ANSWER:
current
voltage
resistance
Part B
Apply the junction rule to the junction labeled with the number 1 (at the bottom of the resistor of resistance
).
Hint B.1
Elements in series
Hint not displayed
Answer in terms of given quantities, together with the meter readings
and
and the current
.
ANSWER:
If you apply the juncion rule to the junction above
, you should find that the ezpression you get is
equivalent to what you just obtained for the junction labeled 1. Obviously the conservation of charge or current
flow enforces the same relationship among the currents when they separate as when they recombine.
Part C
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 Spring '08
 Fr

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