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DELMAR’S Standard Textbook of Electricity - 5th Edition Unit 17 – Alternating Current (AC) Circuits Containing Inductance 1) Inductance a) One of the three primary types of AC loads i) Capacitance and resistance are the other two b) All AC circuits contain some amount of inductance do to the continually changing magnetic field surrounding a conductor i) Usually small, and insignificant until a coil becomes part of the load (1) Relays, motors, transformers, lighting ballasts, and chokes c) Symbolized by the letter d) Characteristics of inductance i) When magnetic lines of flux cut through a coil, a voltage is induced in the coil ii) This induced voltage is always in opposition to the applied voltage (counter-electromotive force) iii) The amount of induced voltage is proportional to the rate of change of current iv) An inductor opposes a change of current e) Calculating the induced voltage i) A 120 VAC source is connected to a coil having 6 ohms of wire resistance ii) An ammeter connected to the circuit indicates that .8 A of current is flowing iii) Ohm’s law can be used to determine the amount of voltage needed to cause .8 A of current to flow in this circuit (a) = × Notes (i) . 8 6Ω = 4.8 (b) Pythagorean’s theorem can be used to calculate the voltage induced in the coil. (i) The induced voltage is therefore equal to the square root of (120 V)2 – (4.8 V)2 or 119.904 V 1. = √120 − 4.8 a. = 119.904 2) Inductive reactance a) From the example above, it is apparent that induced voltage can limit current flow in a circuit in a manner similar to resistance i) This current limiting property is called reactance and is symbolized by the letter ii) To differentiate it from the reactance associated with a capacitor it is labeled (inductive reactance) iii) is measured in ohms just as resistance is and can be calculated when the values of inductance and frequency are known (1) = 2π 3) Schematic symbols a) Air-core inductors b) Iron-core inductors 4) Inductors connected in series a) Calculate like resistors and resistance in series i) = 1 + 2 + 3 … ii) " = # + + $ … 5) Inductors connected in parallel a) Calculate like resistors and resistance in parallel b) = # % % % ' ' … &% &( &) c) " = # % % % ' ' … +& % +& ( +& ) 6) Voltage and current relationships in an inductive circuit a) In a purely inductive circuit, current lags voltage by 90° (ELI) b) Demonstrate I and E waveforms over time to prove 7) Power in an inductive circuit a) A purely inductive circuit dissipates no power except in the resistance of the wire forming the inductor b) Voltage and current have the same polarity for half the time during each cycle and opposite polarity for the other half of each cycle and thereby cancel out i) Mathematically: (1) (+- = + × +) = (−- = + ×– ) = 0 c) Power value for an inductor is reactive power VARsL 8) Reactive power a) Calculate the same as for watts i) 0 = × 9) Q (Quality) of an inductor i) Determined by the ratio of inductive reactance to resistance (1) Inductors having a higher ratio of to are considered to be inductors of higher quality 2 (a) 1 = 3& ii) An inductor with many turns of larger diameter wire will have a higher Q than that same inductor with the same number of turns of small diameter wire