ADV/TEC 3: Introducing Capacitors and Inductors

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## ADV/TEC 3: Introducing Capacitors and Inductors

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**ADV/TEC 3: Introducing Capacitors and Inductors**Introductory mini-lecture**Capacitors**• A capacitor is any two conductors separated by an insulator • Voltage across a capacitor is proportional to the charge on each plate, q = Cv**Capacitors**• Apply voltage v = V0ejωt • Charge builds up on plates, q = C V0 ejωt • A change in voltage drives electrons from one plate to the other around the circuit, producing a current • j indicates a 90o phase difference between i & v i.e., v ‘lags’ i by 90o (or π/2) • Impedance Z = v/i= 1/jωC, Reactance XC = -1/ωC**Capacitors**Currentleadsvoltage**Inductors**• An inductor is a coil of wire usually wound on a magnetic core • Current through the coil produces a magnetic field proportional to the current • As the current changes the magnetic field changes, inducing a voltage that opposes the change in current (by Lenz’s law)**Inductors**• If we apply an alternating voltage v = V0e jωt, then integration gives • The j indicates a 90o phase difference between i& v i.e., v ‘leads’ i by 90o • Impedance Z = v/i= jωL, Reactance XL = ωL**Inductors**Voltage leads current**Real Inductors**• Real inductors have resistance, RL, so the impedance is • Ohm’s Law then becomes: i.e., applied voltage v is the vector sum of vL and vR • Phase angle: