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Discussion Question 6A
P212, Week 6
Two Methods for Circuit Analysis
Method 1: Progressive “collapsing” of circuit elements
In last week’s discussion, we learned how to analyse circuits involving batteries and
capacitors
.
Our
method was to progressively
collapse
groups of capacitors (connected in series or in parallel) into
effective
capacitors.
Once the circuit became simple enough, we could calculate everything about it:
charge and voltage.
Then we worked backwards, breaking up each combination and calculating the
charge and voltage on the individual capacitors.
This week, we will analyze circuits involving
resistors
.
As you know, the formulas for combining
resitors in series and in parallel are “opposite” to those for capacitors.
We also need an expanded set of
rules for “breaking up” combinations of devices:
•
For devices connected in
parallel
:
the
voltage
across them is always the
same
.
•
For devices connected in
series
:
the
charge
and
current
is always the
same
.
But otherwise, the procedure is the same!
(a)
Can you explain the rules stated above in terms of physical principles?
They have simple physical
origins, so they’re easy to remember.
(b)
Consider the circuit shown at right.
All the resistors R
i
have the
same value R.
Find the
current I
4
through resistor R
4
(including its
direction) and the electric
potential V
A
at the indicated point
A
.
Be sure
to express your answers in terms of the given parameters
E
(battery
“EMF” = voltage) and R (resistance of each resistor).
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This note was uploaded on 06/16/2011 for the course PHYS 212 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Kim
 Magnetism

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