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01-circuit

01-circuit - is the voltage diFerence ±rom KirkhoF’s law...

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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 difference U near a resistor. Kirkhoffs 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: ± ± ± ± ± ± x-0 + x-y + x-z = 0 y-x + y-z = 0 z-x + z-9 + z-y = 0 ± ± ± ± ± ± The voltages x, y, z at the corresponding points of the circuit satisfy the linear equations: ± ± ± ± ± ± 3 x-y-z = 0-x + 2 y-z = 0-x-y + 3 z = 9 ± ± ± ± ± ± Can you solve these equations? 1...
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