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ELECTRIC CIRCUITS ECSE-2010 Spring 2003 Class 12. ASSIGNMENTS DUE. Today (Monday): Exam I, 7-9 pm, DCC 308 Homework #4 Due Experiment #3 Report Due Activities 12-1, 12-2 (In Class) Tuesday/Wednesday: Will do Experiment #5 in Class (EP-5) Activity 13-1 (In Class) Thursday:
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ASSIGNMENTS DUE • Today (Monday): • Exam I, 7-9 pm, DCC 308 • Homework #4 Due • Experiment #3 Report Due • Activities 12-1, 12-2 (In Class) • Tuesday/Wednesday: • Will do Experiment #5 in Class (EP-5) • Activity 13-1 (In Class) • Thursday: • Experiment #4 Report Due • Will do Experiment #6 in Class (EP-6) • Activity 14-1 (In Class)
REVIEW • Operational Amplifiers: • High Gain, Differential Voltage Amplifiers: • Real Op Amp Has: • “High” Input Resistance (~10 Mohms) • “Low” Output Resistance (~100 ohms) • “High” Voltage Gain (105-106) • Will Usually Model with Ideal Op Amps: • Ideal Op Amp Has: • Infinite Input Resistance • Zero Output Resistance • Infinite Gain
REVIEW • Operational Amplifiers: • If Add Negative Feedback => Virtual Short at Input • vp= vn; ip = in = 0 • Leads to Useful Circuits • Use Virtual Short and Circuit Analysis to find Output • Effects of Real Op Amps => Use PSpice • Ideal Op Amp is a Very Good Model for a Real Op Amp (Saw this in Computer Project #1)
CIRCUITS WITH R, L, & C • For Resistive Circuits: (No L or C) • v = i R; => v(t) = i(t) R • Resistor does not affect time behavior • Resistors only absorb energy (get hot) • Resistors convert electrical energy to thermal energy
CIRCUITS WITH R, L, & C • R, L, C Circuits: • L = Inductor; C = Capacitor • v, i are now time dependent • v(t) and i(t) may be quite different waveforms • L and C can store electrical energy! • Makes circuits far more interesting • Must find Time Behavior of circuit
CAPACITANCE • See Symbol: • Relationship Between i and v: • ic= C dvc/dt • Measure C in Farads: • 1 farad = 1 amp-sec/volt
CAPACITANCE • DC Steady State: • d /dt = 0 • => iC = CdvC/dt = 0 in DC Steady State • Capacitor is an Open Circuit in DC Steady State • If apply a DC source, Capacitor will charge up to some voltage and stay there in the Steady State
CAPACITANCE • Capacitors in Series: • 1 / Ceq = 1 / C1 + 1 / C2 + 1 / C3 + .. • Similar to Resistors in Parallel • Capacitors in Parallel: • Ceq = C1 + C2 + C3 + … • Similar to Resistors in Series
CAPACITANCE • Energy Stored in Capacitor: • wc = (1/2 ) C vC2 • Energy stored in Electric Field • Voltage Across Capacitor Cannot Change Instantaneously: • Capacitor voltage must be continuous in time • No instantaneous jumps
INDUCTANCE • See Symbol: • Relationship Between i and v: • vL = L diL/dt • Measure L in Henries: • 1 henry = 1 volt-sec/amp
INDUCTANCE • DC Steady State: • d /dt = 0 • => vL= LdiL/dt = 0 in DC Steady State • Inductor is a Short Circuit in DC Steady State • If apply a DC Source, Inductor will have current flowing in it, but no voltage across it in the Steady State
INDUCTANCE • Inductors in Series: • Leq = L1 + L2 + L3 + … • Similar to Resistors in Series • Inductors in Parallel: • 1 / Leq = 1 / L1 + 1 / L2 + 1 / L3 + .. • Similar to Resistors in Parallel
INDUCTANCE • Energy Stored in Inductor: • wL = (1/2 ) L iL2 • Energy Stored in Magnetic Field • Current Through Inductor Cannot Change Instantaneously: • Inductor Current must be continuous in time • No instantaneous jumps
ACTIVITY 12-2 • v = vL = L diL/dt: • iC = C dvC/dt = C dvL/dt • is = iC + iL ; If is = 0; iC = - iL