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ICE 9/27/2004
Math 21b, Oliver Knill
We consider an electric circuit
x
y
z
9
0
which contains a power supply
of 9 volts and is made of 5 resistors. In order to determine the voltage at each point, we need to know
2 laws:
•
Ohms law
U
=
RI
relates the resistance
R
, the current
I
and the voltage diFerence
U
near a
resistor.
•
Kirkhofs law:
tells that the sum of the currents passing to a point is zero.
In our circuit all resistors have resistance 1. Consequently, by Ohm’s law the current through a resistor
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Unformatted text preview: is the voltage diFerence. ±rom KirkhoF’s law we get the equations: ± ± ± ± ± ± x0 + xy + xz = 0 yx + yz = 0 zx + z9 + zy = 0 ± ± ± ± ± ± The voltages x, y, z at the corresponding points of the circuit satisfy the linear equations: ± ± ± ± ± ± 3 xyz = 0x + 2 yz = 0xy + 3 z = 9 ± ± ± ± ± ± Can you solve these equations? 1...
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This note was uploaded on 04/06/2008 for the course MATH 21B taught by Professor Judson during the Spring '03 term at Harvard.
 Spring '03
 JUDSON
 Math, Linear Algebra, Algebra

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