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L35 - Fall 2003 Math 308/501502 3 Modeling and Applications...

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Fall 2003 Math 308/501–502 3 Modeling and Applications 3.5 Electrical Circuits Mon, 22/Sep c 2003, Art Belmonte Summary Electric charge flows through a circuit usually containing a voltage source, resistor, capacitor, and inductor. (Some of these may be absent.) A battery is a constant voltage source; a generator a variable one (typically sinusoidal). An arbitrarily chosen direction around the circuit (say clockwise or counterclockwise) is taken as the positive direction. The opposite direction is regarded as the negative direction. Here is a table of electrical concepts. Using these concepts and the laws that follow permit us to set up a model involving a differential equation that governs the circuit. CONCEPT UNITS C , capacitance F, farads E , voltage V, volts I , current A, amps L , inductance H, henrys q , charge C, coulombs R , resistance , ohms The rate at which charge flows is called the current ; hence I = dq / dt . In the following, E k represents the voltage drop due to component k .
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