ME 140L - Lecture 2 - Circuit Analysis and First Order Systems

ME 140L - Lecture 2 - Circuit Analysis and First Order Systems

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1 MECHATRONICS LAB ME 140L RESISTORS, INDUCTORS, CAPACITORS: CHARACTERIZATION & 1 ST -ORDER CIRCUITS I. CHARACTERIZATION: Constitutive Behavior A. Resistance: V=V(i)—Voltage is a function of current V, voltage i, current (A) R Linear constitutive behavior: V=iR V=Volts, i=Ampere, R=Ohm Power dissipation: R 2 i R 2 V iV P = = =
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2 B. Capacitance: V=V(q)—Voltage is a function of charge q, charge(coulomb) V, voltage 1/C Linear constitutive behavior: V=q/C C=Farad, q=Coulomb Note: dt dV C i dt dq = = Note if voltage across the capacitor is constant (i.e. charge remains the same— dt dV =0), there is no current— Open Circuit Energy Stored: 2 CV 2C q Vdq (idt) V iVdt Pdt E 2 2 = = = = ∫∫ = =
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3 C. Inductance: ) λ i( i = --Current is a function of flux linkage λ, flux linkage(Weber-turns) i, current 1/L Linear constitutive behavior: L λ i = L=Henry, λ =Weber-turns Note: dt di L V dt d λ = = Note if current through the inductor is constant (i.e. flux linkage remains the same), there is no voltage across the inductor— Short Circuit Energy Stored: 2 Li 2L λ id λ i(Vdt) iVdt Pdt E 2 2 = = = = ∫∫ = =
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4 II. CIRCUIT ANALYSIS: Continuity and Compatibility A. Continuity: Kirchoff’s Current Law (KCL) The sum of the currents at a node must be zero. = = N 1 n n 0 i Same as continuity of flow in fluid mechanics for incompressible flow. B. Compatibility: Kirchoff’s Voltage Law (KVL) The net voltage around a closed circuit is zero. = = N 1 n n 0 V Same as compatibility of pressure in fluid mechanics for incompressible flow.
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5 III. CIRCUIT ANALYSIS: First-Order Systems Want to be able to predict how the circuit variables will respond.
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ME 140L - Lecture 2 - Circuit Analysis and First Order Systems

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