Download Lecture 9

Admin:
Mid-term date Friday March 20th.
• Assignments:
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Second graded assignment is posted
Make time for it – it’s a bit tougher than the first one
Due Monday
Use the hints.
One or two of the questions are “tutorial” style, which are designed to
add to the material I’ve covered in class. Use the textbook to help with
these.
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Today
• Using Kirchoff’’s laws
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Kirchhoff’s Rules
Junction rule (Kirchhoff’s current law):
The sum of currents entering a junction
equals the sum of the currents leaving it.
I3=I1+I2
Copyright © 2009 Pearson Education, Inc.
Kirchhoff’s Rules
Junction rule (Kirchhoff’s current law):
This is a result of “conservation of charge”
The charge has to go somewhere!
Copyright © 2009 Pearson Education, Inc.
Kirchhoff’s Rules
Loop rule (Kirchhoff’s
Voltage Law):
The sum of the
changes in potential
around a closed loop
is zero.
0 = 12 - 400I - 290I
Copyright © 2009 Pearson Education, Inc.
Kirchhoff’s Rules
Why does the loop rule work?
•This is the result of “conservation of energy”
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All points of a circuit react instantaneously (at the speed of light)
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A “source” provides energy
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But Voltage is energy/charge (Joules/Coulomb)
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So, a 12V source provides 12 Joules of energy for each
Coulomb of charge
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The energy is used up by transporting charge through
resistance
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If the voltage of the source changes, the rate of charge transport
changes
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If the resistance changes, the rate of charge transport changes
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V=IR !
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http://regentsprep.org/Regents/physics/phys03/apotdif/
Copyright © 2009 Pearson Education, Inc.
Kirchhoff’s Rules
Problem Solving: Kirchhoff’s Rules
1. Label each current, including its direction.
2. Identify unknowns.
3. Apply junction and loop rules; you will
need as many independent equations as
there are unknowns.
4. Solve the equations, being careful with
signs. If the solution for a current is
negative, that current is in the opposite
direction from the one you have chosen.
Copyright © 2009 Pearson Education, Inc.
Kirchhoff’s Rules
Example: Using Kirchhoff’s rules. (see p685-6)
Calculate the currents I1, I2, and I3 in the three
branches of the circuit in the figure.
1. Label currents
2. 3 unknowns
3a. 1 Junction Rule
3b. 2 Loop Rules
4. Solve
Copyright © 2009 Pearson Education, Inc.
Notes on Kirchhoff analysis
• The unknowns may not always be currents
- they could be voltages or resistances –
but the procedure is exactly the same
• If solutions to currents or voltages are
negative, this means the real direction is
opposite to what you originally defined
• To deal with current sources: the current is
known, but assign an unknown voltage
across it which has to be solved
Copyright © 2009 Pearson Education, Inc.