2 MA 36600 LECTURE NOTES: MONDAY, APRIL 6 Circuits. Consider a circuit that contains three devices: i. an inductor (which behaves like a mass), ii. a resistor (which behaves like friction), and iii. a capacitor (which behaves like a spring). Such a circuit is called an LRC Circuit . Let Q = Q ( t ) denote the charge at time t , I = I ( t ) denote the current at time t , and V = V ( t ) denote the voltage at time t . We have the following relations: i. For an inductor, V inductor ∝ dI inductor dt = ⇒ V inductor = L · dI inductor dt . The constant L is called the inductance . ii. For a resistor, V resistor ∝ I resistor = ⇒ V resistor = R · I resistor . The constant R is called the resistance . (This is called Ohm’s Law .) iii. For a capacitor, V capacitor ∝ Q capacitor = ⇒ V capacitor = 1 C · Q capacitor = ⇒ dV capacitor dt = 1 C · I capacitor . The constant C is called the capacitance . The constants L , R , and C motivate the name “ LRC Circuit.” In order to form di±erential equations, we need an equivalent of Newton’s Laws of Motion for circuits.
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