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Engineering Practice Electric Fitting Resistance • Electrical resistance is the ratio of voltage drop across a resistor to current flow through the resistor. • Polarities are governed by the passive sign convention. v R i R i + v - I, V & R Current = voltage / resistance • I=V/R V=IxR Definitions • Voltage = potential energy / unit charge, units = Volts • Current = charge flow rate, units = Amps • Resistance = friction, units = Ohms Example • Voltage drop when current flows through resistor • V1 - V2 = I R V1 I R V2 Power Consumed by Resistors • Resistors consume power. • v and i are both positive or both negative. R i + v - p v i v R i v i R Creating a Circuit Model • A circuit model is usually two or more circuit elements that are connected. • A circuit model may have active elements (sources) as well as passive elements (such as resistors). • By the assumption that electric signal propagation is instantaneous in a circuit, our circuit model has lumped parameters (A lumped system is one in which the dependent variables of interest are a function of time alone. In general, this will mean solving a set of ordinary differential equations (ODEs)). Schematics • Symbols represent circuit elements • Lines are wires + Resistor Battery Sample circuit Ground V + I R Ground voltage defined = 0 Example of a Circuit Model 1000 ft AWG 14 Copper Wire 100 W Lamp 120 V Battery 0.25 2.57 144 120 V 2.57 Kirchhoff’s Voltage Law • The sum of the voltage drops around a closed path is zero. • Example: -120 + V1 + V2 + V3 + V4 = 0 0.25 + V1 - 2.57 + V2 - 120 V 2.57 - V4 + + V3 - 144 Kirchhoff’s Current Law • A node is a point where two or more circuit elements are connected together. • The sum of currents associated with a node is zero. I1 I4 I3 I2 Parallel And Series Resistors Series circuit V = R1 I + R2 I = Reff I Reff = R1 + R2 Series • Same current flows through all Parallel • Same voltage across all R1 V Parallel circuit I = V/R1 + V/R2 = V/Reff 1/Reff = 1/R1 + 1/R2 + I R2 I V + R1 I1 R2 I2 Note: these points are connected together Resistive voltage divider • Series resistor circuit • Reduce input voltage to desired level • Advantages: – simple and accurate – complex circuit can use single voltage source Resistive divider • Disadvantage: I = Vin/Reff = Vout/R2 – dissipates power Vout =I Vin (R2 / (R1 + R2) ) – easy to overload Vin Vout – need Rload << R2 + R1 R2 I New schematic symbol external connection Variable voltage divider • Use potentiometer (= variable resistor) • Most common: constant output resistance Variable voltage divider Vout = Vin (Rout / (Rvar + Rout) ) New schematic symbol: potentiometer I Vin + Vout Rvar Rout I Impedance Impedance : • Definition : Impedance is the current resisting and impeding characteristic of load or conductor in an AC Circuit. • Symbol for Impedance: Z Z = R + jXl - jXc Where, jXl = Zl and, -jXc = Zc • Unit for Impedance: Ohms or s. Revisit Ohm’s Law Ohms Law: • Mathematical Statement of the Ohm’s Law: V = I R for DC circuits V = I Z for AC Circuits Note: BOLD letters, in general, represent Vectoral quantities “GROUND” Please float your ideas Three phase systems AC-generator • An AC generator consists of a coil wound on a metallic core that rotates in a magnetic field. • The ends of the coil are connected to a pair of slip rings that are the means to transport the voltage to the external circuit. Single phase Vs Three phase • The horsepower rating of three phase motors and the KVA (kilo-volt-amp) rating of three-phase transformers is about 150% greater than that for single-phase motors or transformers with a similar frame size. Single phase Vs Three phase • The power delivered by a single-phase system falls to zero three times during each cycle. Whereas the power delivered by a three-phase system never falls to zero. The following figure elaborates it. Wye or Star connection • The wye or star connection is made by connecting one end of each of the three-phase windings together. • The common point is kept as the ground or reference. • The voltage measured across a single winding or phase is known as the phase voltage. • The voltage measured between the lines is known as line voltage. Wye or Star connection • In a wye connected system, the line voltage is higher than the phase voltage by a factor of 1.732. Phase current is equal to line current. Delta Connection • In the delta connection, line voltage is equal to the phase voltage. • The line current of a delta connection is higher than the phase current by a factor of 1.732. Mains circuits Household electric wiring plan for a flat: electric mains supply company’s cable N main fuse kW h meter consumer unit mains switch L mains socket 30 A 5 A 15 A 30 A cable water heater air-conditioner cable cable lighting circuit ring main cable 2-way switches mains socket mains socket Mains circuits main supply electric cable company’s main fuse kilowatt-hour meter in parallel consumer unit (‘fuse box’) lamps water heater airconditioner All electrical appliances are connected in parallel. Why? faults in one circuit will not affect other circuits. Mains circuits mains supply cable electric company’s main fuse kilowatt-hour meter consumer unit (‘fuse box’) lamps • Each circuit branch has L, N & E wires. water heater airconditioner • Earth wires are connected to an earthing electrode buried underground. consumer unit (‘fuse box’) It has a main switch: one can switch off whole circuit for repair work or in case of emergency each circuit is fitted with a fuse or circuit breaker Lighting circuit 5A • 1 branch for ceiling lamps: lighting circuit • Each lamp is controlled by a switch on wall • Protected by 5 A fuse lighting circuit Two-way switches The lamp can be switched on at the bottom of the staircase & then switched off at the top, & vice versa. Two-way switches The lamp can be switched on at the bottom of the staircase & then switched off at the top, & vice versa. on off