MA 36600 MIDTERM #2 REVIEW 5 • Let Q = Q ( t ) denote the charge in an electric circuit at time t ; it is measured in coulombs. Similarly, I = dQ dt denotes the current; it is measured in amperes. We think of Q as the “displacement” u ( t ), and I as the “velocity” u ° ( t ). Say that we have four objects in our circuit: i. Inductor (which acts like the mass): The voltage across an inductor is proportional to the change in the current: V inductor ∝ dI dt = ⇒ V inductor = L dI dt for some positive constant L . We call L the inductance ; it is measured in henrys. ii. Resistor (which acts like a damping force): Ohm’s Law asserts that the voltage across a resistor is proportional to the current: V resistor ∝ I = ⇒ V resistor = IR for some positive constant R . We call R the resistance ; it is measured in ohms. iii. Capacitor (which acts like a spring): The voltage across a capacitor is proportional to the charge: V capacitor ∝ Q = ⇒ V capacitor = 1 C Q for some positive constant C . We call C the capacitance ; it is measured in farads.
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This note was uploaded on 11/30/2011 for the course MATH 366 taught by Professor Edraygoins during the Spring '09 term at Purdue.