Principles Lesson 1 - Lecture notes 6 PDF

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Learning the basic principles of electrical engineering...

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OHM’S LAW Electrical Engineering Technology Principles 1 Overview of course – DC Circuits ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓

Ohm’s Law Series circuits Parallel circuits Series-parallel circuits Superposition Theorem Thevenin’s Theorem Kirchhoff’s Law Wheatstone Bridge Star-Delta Transposition

Electrical engineering can be summarized into four main categories: a. The production of electrical energy b. The transmission of electrical energy c. The application of electrical energy d. The control of electrical energy

In an electrical circuit, at constant temperature, the current in the circuit is directly proportional to the applied voltage but is inversely proportional to the circuit resistance. Conductors with a positive temperature coefficient tend to have an increase in resistance with respect to an increase in temperature. Ohm’s law states that when the supply voltage is increased the current will have a corresponding increase. Conversely when the voltage is decreased the current will decrease as well. The current and resistance relationship shows that with an increase in resistance the current is decreased but when the resistance is decreased the current will increase.

Electrical Terminology A basic electrical system has four constitutional parts as follows: a. The source The function of the source is to provide the energy for the electrical system. A source is thought of as a battery or a generator. b. The load The function of the load is to absorb the electrical energy supplied by the source. Most domestic electrical equipment constitutes loads. Common examples of loads include lamps and heaters. c. The transmission system This conducts the energy from the source to the load. Typical transmission system consists of insulated wires. d. The control system As the name suggests, its function is to control. The most simple control is a switch which permits the energy to flow or else interrupts the flow of electrons.

Current (I) ✓ The flow of electrons through an electrical circuit ✓ Current is measured in amperes (A) ✓ Instrument for measuring current is the ammeter ✓ Current = voltage ÷ resistance ✓ I = V/R Voltage (V) ✓ the force that pushes electrons through a circuit ✓ voltage is measured in volts (V) ✓ Instrument for measuring voltage is the voltmeter ✓ Voltage = current x resistance ✓ V=IxR Resistance (R) ✓ The opposition to electron flow in a purely resistive circuit ✓ Resistance is measured in Ohms (Ω) ✓ Resistance is measured with an ohmmeter ✓ Circuit must be dead when using an ohmmeter ✓ Resistance = voltage ÷ current ✓ R = V/R

Power (P) ✓ The rate of doing work ✓ Measured in watts (W) ✓ Power = V x I ✓ P= I2R ✓ P = V2/R

Series Circuit Laws ✓ A series circuit is one in which components are connected one after another to form one current path. ✓ The value of current in a series circuit is the same at every point in the circuit ✓ The sum of the voltage drops across each component in a series circuit will equal the source or applied voltage ✓ The sum of all resistances in a series circuit equals the total resistance. ✓ If there is a break at any point in a series circuit, the entire circuit becomes inoperative or it shuts down. ✓ Applications for series circuits include Christmas lights, voltage dividers, tuning circuits, etc.

3. Five resistors are connected in series and there is a current of 3 A into the first resistor. What amount of current into the second resistor?

4. Three resistors behave as 1 : 2 : 3. The applied voltage is 24 v. calculate the voltage across each resistor. 5. Resistors of 5Ω, 10Ω and 15Ω are connected in series. Find (a) the total resistance; (b) the circuit current if the circuit is powered by a 60 V source; and (c) the voltage across resistor two (10Ω). 6. A heating coil has a resistance of 40Ω; a voltage of 220 V is applied. Calculate the current. 7. A 60 w bulb draws a current of 273 mA at 220 V. what is the resistance of the bulb? 8. An ammeter with a measuring range of 6 A has an internal resistance of 60 mΩ. what is the voltage drop at full-scale deflection? 9. A light bulb (110 V/40 W) draws 0.36 A. it is to be connected to the mains (220V). calculate the required series resistance.

10. An electrical circuit consists of a 12Ω and 18Ω resistor connected in series. If the circuit is powered by a 30V source, determine a. The total resistance b. The circuit current c. The voltage drop across each resistor

Exercises 1. Define a series circuit and state the voltage, current and resistance characteristics of the circuit. 2. State two principal disadvantages and applications of a series circuit.

11. An electrical circuit consists of a 6Ω and 12Ω resistor connected in series. If the circuit is powered by a 36V source, determine a. The total resistance b. The circuit current c. The voltage drop across each resistor 12. An electrical circuit consists of a 4.6Ω and 10.5Ω resistor connected in series. If the

circuit is powered by a 60V source, determine: a. The total resistance b. The circuit current c. The voltage drop across each resistor 13. The total resistance of two resistors connected in series is 65Ω. If the value of one resistor is 27Ω, determine the value of the next resistor 14. The total resistance of two resistors connected in series is 175Ω. If the value of one resistor is 78Ω, determine the value of the next resistor

coil is to be limited to 2 A, calculate the resistance of the resistor to be connected in series with the coil.

21. It is required to deliver a current of 30A to a heater circuit at a distance from the main fuse board. Find the voltage at the heater terminals if the supply voltage at the main fuse board is 240V and the resistance of the cable is 0.25 Ω. Calculate (a) the wattage of the heater and (b) the power lost in the cable.

22.

15. The total resistance of three resistors connected in series is 75Ω. If the value of R1= 30Ω and R2= 15Ω, determine the value of the R3. 16. Three resistors of 2Ω, 3Ω and 5Ω are connected in series and a current of 2 A flows through them. Calculate the p.d. across each resistor and the total supply voltage. 17. The lamps of a Christmas tree are connected in series. If there are 20 lamps and each lamp has a resistance of 25Ω, calculate the total resistance of the set of lamps and the current taken from the 120 V supply.

Determine: a. R1 (the value of resistor 1) b. VR2 (voltage across resistor 2) c. PR3 (power dissipated in resistor 3) d. RT (total resistance) e. PT (total power) 23.

18. A halogen lamp has an operating voltage of 12 V at a current of 8.3A. The lamp is to be connected to a 220 V. Calculate the value of a resistor to be connected in series with the lamp. 19. Three lamps are connected in series over a 120V supply and take a current of 1.5 A. If the resistance of two of the lamps is 30Ω each, what is the resistance of the third lamp? 20. The field of a dc generator is has a resistance of 60Ω and is supplied from a 240 V source. Given that the current in the

Determine: a. VR2

(c) RT

b. R1

(d) PR1

24.

30. Two resistors are in series: a 5.6 k resistor and a 4.7 k resistor. The voltage drop across the 5.6 k resistor is 10 V. determine the voltage across the 4.7 k resistor.

Determine: a. b. c. d. e.

The current The missing voltage drops The supply voltage The total resistance Power across each resistor

25. A 2400W/240V heater is connected to a distribution board some 25 m away from the source. If the cable has a resistance of 0.5Ω, determine (a) the useful voltage applied to the heater and (b) the resulting power of the heater.

26. Four equal resistors are connected in series. Let the current in this series connection be 50% of the current that would flow if the voltage across one of the resistors was 12 V. find the voltage that must be applied across the series connection. 27. The following resistors (one each) are connected in a series circuit: 470 Ω, 680 Ω, 1kΩ, and 1.2kΩ. The voltage source is 20 V. determine the approximate current through the 680Ω resistor. 28. A string of five series resistors is connected across a 6 V battery. Zero voltage is measured across all resistors except R3. Determine the voltage across R3. 29. A certain series circuit consists of a 1/8 W resistor, a 1/4 W resistor, and a 1/2 W resistor. The total resistance is 1200 . If each resistor is operating in the circuit at its maximum power dissipation, determine the total current flow in the circuit....