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26. DC Circuits
Assignment is due at 2:00am on Wednesday, February 21, 2007
Credit for problems submitted late will decrease to 0% after the deadline has passed.
The wrong answer penalty is 2% per part. Multiple choice questions are penalized as described in the online help.
The unopened hint bonus is 2% per part.
You are allowed 4 attempts per answer.
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 describest he conservation of which quantity? Note that this rule applies only to circuits that are
in steady state.
Hint A.1 At the junction
Hint not displayed
ANSWER:
Answer not displayed
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
Answer in terms of given quantities, together with the meter readings
and
and the
current
.
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Part C
Apply the loop rule to loop 2 (the smaller loop on the right). Sum the voltage changes across each circuit element
around this loop going in the direction of the arrow. Remember that the current meter is ideal.
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This note was uploaded on 11/02/2009 for the course MASTERING PHYS taught by Professor All during the Spring '09 term at Kettering.
 Spring '09
 All

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