2. Engineering Practice Electric Fitting

3. 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.

4. Current = voltage / resistance I = V / R V = I x R 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 V 1 - V 2 = I R I R V1V1 V2V2 I, V & R

5. Power Consumed by Resistors Resistors consume power. v and i are both positive or both negative.

6. 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)).

7. Schematics Symbols represent circuit elements Lines are wires + Battery Resistor Ground + V R I Sample circuit Ground voltage defined = 0

8. Example of a Circuit Model

9. Kirchhoff’s Voltage Law The sum of the voltage drops around a closed path is zero. Example: -120 + V 1 + V 2 + V 3 + V 4 = 0

10. 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.

11. Parallel And Series Resistors Series Same current flows through all Parallel Same voltage across all + Note: these points are connected together I V R1R1 R2R2 Series circuit V = R 1 I + R 2 I = R eff I R eff = R 1 + R 2 Parallel circuit I = V/R 1 + V/R 2 = V/R eff 1/R eff = 1/R 1 + 1/R 2 + V R1R1 R2R2 I1I1 I2I2 I

12. Resistive voltage divider Series resistor circuit Reduce input voltage to desired level Advantages: –simple and accurate –complex circuit can use single voltage source Disadvantage: –dissipates power –easy to overload –need R load << R 2 New schematic symbol external connection + V in R1R1 R2R2 I I V out Resistive divider I = V in /R eff = V out /R 2 V out = V in (R 2 / (R 1 + R 2 ) )

13. Variable voltage divider Use potentiometer (= variable resistor) Most common: constant output resistance + V in R var R out I I V out Variable voltage divider V out = V in (R out / (R var + R out ) ) New schematic symbol: potentiometer

14. 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 + jX l - jX c Where, jX l = Z l and, -jX c = Z c Unit for Impedance: Ohms or  s.

15. 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

16. “GROUND” Please float your ideas

17. Three phase systems

18. 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.

19. 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.

20. 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.

21. 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.

22. 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. Wye or Star connection

23. 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.

24. Mains circuits Household electric wiring plan for a flat: mains supply cable mains socket cable ring main mains socket cable electric company’s main fuse cable consumer unit lighting circuit 30 A5 A15 A30 A water heater air-conditioner kW h meter 2-way switches N L mains switch

25. main supply cable electric company’s main fuse kilowatt-hour meter consumer unit (‘fuse box’) All electrical appliances are connected in parallel. Why? faults in one circuit will not affect other circuits. water heater air- conditioner lamps in parallel Mains circuits

26. mains supply cable electric company’s main fuse kilowatt-hour meter consumer unit (‘fuse box’) Each circuit branch has L, N & E wires. Earth wires are connected to an earthing electrode buried underground. water heater air- conditioner lamps Mains circuits

27. It has a main switch: consumer unit (‘fuse box’) each circuit is fitted with a fuse or circuit breaker one can switch off whole circuit for repair work or in case of emergency

28. Lighting circuit 1 branch for ceiling lamps: Protected by 5 A fuse 5 A lighting circuit Each lamp is controlled by a switch on wall

29. The lamp can be switched on at the bottom of the staircase & then switched off at the top, & vice versa. Two-way switches

30. The lamp can be switched on at the bottom of the staircase & then switched off at the top, & vice versa. on off