So I just had an idea about visualizing circuits that seems straightforward and useful, but I can't find any mention in Google of someone having used it before. Surely this is not a new idea
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You'd color-code them or something - resistors are red, diodes are purple, something like that.
One neat property of the rectangle visualization thing - if I have a circuit diagram that I can draw as a planar graph (no crossing wires/edges) and I've done the math to determine the current/voltage on each component, then if I replace all the component symbols with their equivalent correctly-scaled rectangles all the rectangles for the circuit can be packed into one large rectangle.
Or equivalently, say I have a rectangle that is 6 volts tall and 3 amps wide. The rectangle itself represents a resistor with a value of 2 ohms (6/3) connected to a 6 volt power supply - you can think of it as current flowing "into" the resistor from the top and out the bottom. If I divide that 6x3 rectangles into two 3x3 rectangles, that represents two 1 ohm (3/3) resistors in series (and each is obviously dissipating half the power of the 2-ohm resistor because they're half the size). If I divide it into two 6x1.5 rectangles, that represents two 4 ohm (6/1.5) resistors in parallel, both again dissipating half the power.
Continuing that idea, _every_ possible way of subdividing that rectangle into smaller rectangles represents a valid resistor network whose equivalent resistance is 2 ohms - the packed-rectangle diagram is both a representation of the circuit and a simulation of current flow through the circuit.
If I subdivide my original rectangle into 2-volt-tall rectangles, I can replace one of the resistor rectangles with a red LED rectangle, and now I have a circuit that lights a LED (and correctly simulates the currents / resistances needed to light the LED with a current of 3 amps (big LED ;) ))
One neat property of the rectangle visualization thing - if I have a circuit diagram that I can draw as a planar graph (no crossing wires/edges) and I've done the math to determine the current/voltage on each component, then if I replace all the component symbols with their equivalent correctly-scaled rectangles all the rectangles for the circuit can be packed into one large rectangle.
Or equivalently, say I have a rectangle that is 6 volts tall and 3 amps wide. The rectangle itself represents a resistor with a value of 2 ohms (6/3) connected to a 6 volt power supply - you can think of it as current flowing "into" the resistor from the top and out the bottom. If I divide that 6x3 rectangles into two 3x3 rectangles, that represents two 1 ohm (3/3) resistors in series (and each is obviously dissipating half the power of the 2-ohm resistor because they're half the size). If I divide it into two 6x1.5 rectangles, that represents two 4 ohm (6/1.5) resistors in parallel, both again dissipating half the power.
Continuing that idea, _every_ possible way of subdividing that rectangle into smaller rectangles represents a valid resistor network whose equivalent resistance is 2 ohms - the packed-rectangle diagram is both a representation of the circuit and a simulation of current flow through the circuit.
If I subdivide my original rectangle into 2-volt-tall rectangles, I can replace one of the resistor rectangles with a red LED rectangle, and now I have a circuit that lights a LED (and correctly simulates the currents / resistances needed to light the LED with a current of 3 amps (big LED ;) ))
Starting to get the idea?
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