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Unformatted text preview: Basic Circuit Definitions, Elements and Properties – AC Circuits EE 201
DePiero / CalPoly State University Common Components Appearing in AC Electrical Circuits • Components in DC circuits are also used in AC circuits o Sources, resistors, switches… • AC Sources produce alternating currents or voltages. Often sources operate at some given frequency (e.g. 60Hz for US power systems). Analysis on a per frequency basis. • AC circuits also include energy storage elements o Capacitor: Stores energy in form of a voltage o Inductor: Stores energy in form of a current Capacitor • Stores energy in an electrical field, with an associated voltage • Capacitor has parallel plates separated by a dielectric material. Capacitors give up charge in a process of polarizing a dielectric material. Net effect accumulates +,
charges on plates developing a voltage across the device. • Capacitance, C, measured in Farads (F) Transient Currents Due to Charging Capacitor Fixed charge on cap Moving charge (current) Voltage source drives positive charge into circuit from upper (+) node of source and draws charge into lower (
) node. However moving charges do not pass through the capacitor. Rather, (+) charges accumulate on the top plate. The lower plate of cap gives up (+) charges into the circuit in the process of polarizing the dielectric material. This results in (
) charges remaining fixed at the cap. Pairs of (+/
) charges separate in cap to provide current flow out of device. A voltage is developed across the capacitor due to the separation of stored charges. This voltage increases as charge accumulates. Eventually capacitor voltage equals source voltage, stopping current flow. This is (1st order differential) style of the transient charging current. AC Steady State Currents With sinusoidal excitation, the capacitor charges and discharges with each cycle of the source. In steady state, the peaks of the source and cap voltage (current) remain constant. Capacitor – Circuit Properties • Voltage V stored due to charge Q: Q = C V • Energy stored due to charge: Wc = (1/2) C V2 • I
V relationship: i(t) = C dv/dt dQ/dt = i(t) = C dv/dt • Voltage of a capacitor cannot change instantaneously. • Capacitors in parallel add. Caps in series combine like resistors in parallel. • Ideal capacitor is an open circuit to DC current • Practical limit: Capacitors have a maximum voltage Analogy: Hydraulic accumulator, a pressure ‘shock absorber’ Gas Liquid Inductor • Stores energy in a magnetic field, due to an associated current • Coil generates magnetic field (concentrated by metallic core). When current drops, magnetic field reduces, restoring electrical current. • Inductance, L, measured in Henrys (H) • Transients of a circuit containing an inductor are due to the inductor resisting changes in current. Inductor – Circuit Properties • Energy stored due to current: WL = (1/2) L I2 • I
V relationship: v(t) = L di/dt • Current of an inductor cannot change instantaneously. • Inductors in series add. Inductors in parallel combine like resistors in parallel. • Ideal inductor a short to DC current (a wire with no resistance) • Practical limit: Capacitors have a maximum voltage Analogy: Momentum of a moving fluid Transformer • Energy conversion element • Analogy: Gears or a lever • Transformer alters form of power, one side of transformer has high V, low I; while the other side has low V, high I. AC only. • Ideal transformer has no power loss P=VI same each side RMS Signal Intensity The average signal value is useful at times when describing some time
varying signals (such as a periodic rectangular waveform). However sinusoids have zero mean value. Thus the average is not a useful way to describe signal intensity. The ‘Root Mean Square’ (RMS) method is often used to describe the effective signal intensity. VRMS =
What do these devices look like? Resistors Dissipate electrical energy, converting it to heat 1
T ∫ € T
0 v 2 ( t ) dt Capacitors Store energy in an electrical field, with an associated voltage Inductors (or coils) Store energy in a magnetic field, with an associated current Transformers Convert the form of AC electrical energy ...
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 Spring '08
 ARAKAKI

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