CHAPTER 1

CHAPTER 1INTRODUCTION TO ELECTRICAL CIRCUITS

LEARNING OUTCOMESUnderstand basic Electrical Quantities (units and symbols)

Explain types of Electrical Circuits

Understand Ohms Law

Understand Electrical Power

Understand the characteristics of series and parallel circuits

ELECTRICAL QUANTITIES Electromotive Force ( EMF ) Electromotive Force is the voltage produced by an electric battery or generator in an electrical circuit or more precisely, the energy supplied by a source of electric power in driving a unit charge around the circuit. Unit: voltSymbol: VCharge Electric charge is a physical property of matter which causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two negatively charged objects. Positively charged objects and negatively charged objects experience an attractive force.

Unit: coulomb (C)Symbol: QCurrent Electric current is a flow of electric charge through a medium.

Potential Energy ( Voltage )Voltage is a measure of the energy of electricity, specifically, it is the energy per unit charge.

Unit: ampere (A)Symbol: IUnit: volt (v)Symbol: VResistance Resistance is defined as the ability of a substance to prevent or resist the flow of electrical current.

Unit: ohm () Symbol: RFACTORS THAT AFFECT THE RESISTANCE OF CONDUCTOR MATERIALS Material (Resistivity) Resistance of a uniform conductor is directly proportional to its resistivity.

Length Resistance of a uniform conductor is directly proportional to its length.

Cross-sectional area Resistance of a uniform conductor is inversely proportional to its cross- sectional.

Temperature The resistance of a metallic conductor increases as the temperature increases. RELATIONSHIP BETWEEN RESISTANCE, LENGTH, CROSS-SECTIONAL AREA AND RESISTIVITY USING THE FORMULA

Example 1 A length of copper is 125m long, having an area of 2.0mm2 has a specific resistance of 1.67x10-8. What is the resistance?

Example 2: A copper wire has a length of 160 m and a diameter of 1.00 mm. If the wire is connected to a 1.5-volt battery, how much current flows through the wire? Given the copper = 1.72 x 10-8 m.

The area is the cross-sectional area of the wire. This can be calculated using

The resistance of the wire is then:

A = r2 = (0.0005) 2 = 7.85 x 10-7 m2R = L/ A = (1.72 x 10-8 )(160) / 7.85 x 10-7 m2 = 3.50 1.1ELECTRICAL QUANTITIESFactors That Affect The ResistanceUnits And SymbolsElectromotive Force ( EMF ) Resistance Charge Potential Energy Current Material (Resistivity) LengthTemperature Cross-sectional area

Types of Electrical CircuitsSimple CircuitsIt is also known as basic circuit as shown in figure below. It is close circuit which allows flow of current perfectly from source to other components and back to the source. The circuit consists of voltage supply (V), electric current (I) and resistance (R).

Simple CircuitComplex CircuitsA complex set of electronic components and their interconnections that are etched or imprinted onto a tiny slice of semiconducting material.

Complex CircuitShort Circuits A circuit element with resistance approaching zero is called short circuit. It would expect a short circuit to allow for unimpeded flow of current. A SHORT circuit occurs when the LOAD is by passed. Because the LOAD helps to restrict and control electron flow, this results in an uncontrolled movement of electrons which causes damage to the CONDUCTOR or the SOURCE due to overheating.

Short CircuitOpen Circuits A circuit element with resistance approaching infinity is called open circuit. It would expect no current to flow through an open circuit. An OPEN circuit occurs when part of the conductor is missing. This can be intentional (for example - controlling a light with a switch) or accidental (a broken wire). This results in NO electron flow in the circuit.

Open CircuitUse of Voltmeters, Ammeters and OhmmetersVoltmeterThe Voltmeter is a device that can measure the voltages across the a circuit element. The voltmeter need to be connected across the element whose voltages we wish to measure.

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A voltmeter also must fulfill two requirement:

i.The voltmeter must be connected in parallel with the element whose voltage to be measured.

ii.The voltmeter should draw no current away from the element whose voltage to be measured, or else it will not measuring the true voltages across the element. Thus, an ideal voltmeter has infinite internal resistance.

Ammeter

The ammeter is a device that when connected in series with the a circuit element, can measure the current flowing through the element. Two requirements are evident for obtaining a correct measurement of current:

i.The ammeter must be placed in series with the element whose current is to be measured.ii.The ammeter should not restrict the flow of the current (i.e cause the voltage drop), or else it will not be measuring the true current flowing in the circuit. An ideal ammeter has zero internal resistance.

Ohmmeter

The ohmmeter is a device that when connected across a circuit element, can measure the resistance. The resistance of an element can be measured only when the element is disconnected from any other circuit.

1.2 ELECTRICAL CIRCUITsimple circuitscomplexcircuitsshort circuitsopencircuitsFunctionVOLTMETERAMMETEROHMMETEROhms LawOhm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points, and inversely proportional to the resistance between them. Current is the rate of flow of electrons through a circuit. Voltage is the electrical pressure. Resistance is the opposition to the flow of electrons in a material.

V = volts I = amperesR = ohms

Relationship that Voltage Is Directly Proportional to Current

V = I x R I = V R R = V IExample 1

The current flow through the circuit of the flashlight is 0.1 amperes. The power source is two D cells, providing 3 volts.What is the resistance of the light bulb?

R = V ; = 3V I 0.1A = 30

Example 2

What is the current flow through a light bulb of 30-ohm resistance when the voltage drop across the light bulb is 12 volts?

I = V ; = 12V R 30 = 0.4A

I = V RV = I x R R = V I1.3OHMSLAWV = volts I = amperesR = ohms

ELECTRICAL POWERElectrical power is defined as the amount of electric current flowing due to an applied voltage. It is the amount of electricity required to start or operate a load for one second.

Unit: watts (W)Symbol: PClarify that Electrical Power can be Delivered as Defined by Derivation of the Voltage and the Direction of the Current.

P = VI V = I R ;So,P = V I = (I R)I = I2 R P = I2 R P = V2 RI = V/R ;So,P = V I = V(V/R)P = V2 RUse of WattmeterWattmeter

The wattmeter is an instrument that provides a measurement of the power dissipated by a circuit element, since the wattmeter is in effect made up of a combination of a voltmeter and an ammeter. In effect, the wattmeter measure the current flowing through the load and simultaneously, the voltages across it and multiplies the two to provide a reading of the power dissipated by the load.

Solve Problem Related to Electrical power

Example 1

A toaster has current of 5A and home voltage supply is 240V. Calculate the power consumption needed for the toaster.

P = VI = 240 X 5 = 1200 W = 1.2 kW1.4ELECTRICAL POWERUnit: watts (W)Symbol: PP = VI P = I2 R P = V2 RSERIES AND PARALLEL CIRCUITSSeries CircuitCurrent through each load resistance is the same.Total current in the circuit is the sum of load resistance.Total voltages drop equal the source current.

+_BulbParallel CircuitVoltages across each load resistance is the same.Current flow through each load will be different if the load resistance is different. Equivalence resistance of the circuit is less than the lowers load resistance.Total current in the circuit equal the sum of the branch current.

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FORMULAS USED IN SERIES CIRCUITSCurrent in Series Circuit is:

Voltage in Series Circuit is:

Resistance in Series Circuit is:IT = I1 = I2 = I3 = = INVT = V1 + V2 + V3 + + VNRT = R1 + R + R3 ++ RN2

Example 1What is the total resistance?What is the current in the circuit? What is the potential difference across each resistor?

a. total resistanceb. current in the circuit

Vc. potential difference across each resistor

Example 2

The diagram shows a series circuit.

a. What is the total resistance? b. What is the current in the circuit? c. What is the potential difference across the 50 ohm resistor?

a. Total resistance = 30 + 40 + 50 = 120 b. Current, I = V/R = 12 V/120 = 0.1 A c. Voltage, V = IR = 0.1 AX50 = 5 V

FORMULAS USED IN PARALLEL CIRCUITSCurrent in Parallel Circuit is:

Voltage in Parallel Circuit is:

Resistance in Parallel Circuit is:IT = I1 + I2 + I3 + + INVT = V1 = V2 = V3 = = VN

Example 1This circuit is a parallel circuit

1/Rt = 1/30 + 1/40 + 1/50 = 47/600 Rt = 600/47 = 12.8 Current, I = V/R = 12 V / 12.8 = 0.94 A Current, I = V/R = 12 V / 30 = 0.4 A

What is the total resistance?What is the current in the circuit?What is the current through the 30 Ohm resistor? CURRENT DIVIDER RULECurrent Divider RuleWe can use Current Divider Rule for determine current value in every junction in circuit Let's analyze a simple parallel circuit, determining the branch currents through individual resistors:

2.Knowing that voltages across all components in a parallel circuit are the same, we can fill in our voltage/current/resistance table with 6 volts across the top row: 3.Using Ohm's Law (I=V/R) we can calculate each branch current:

Knowing that branch currents add up in parallel circuits to equal the total current, we can arrive at total current by summing 6 mA, 2 mA, and 3 mA:

The final step, of course, is to figure total resistance. This can be done with Ohm's Law (R=V/I) in the "total" column, or with the parallel resistance formula from individual resistances. Either way, we'll get the same answer:

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V

VVOLTAGE DIVIDER RULEVoltage Divider RuleWe can use volatge divider rule in order to calculate the value of individual voltage through every resistor in series circuit .Let's analyze a simple series circuit, determining the voltage drops across individual resistors:

2. From the given values of individual resistances, we can determine a total circuit resistance, knowing that resistances add in series:

VFrom here, we can use Ohm's Law (I=E/R) to determine the total current, which we know will be the same as each resistor current, currents being equal in all parts of a series circuit:

Now, knowing that the circuit current is 2 mA, we can use Ohm's Law (V=IR) to calculate voltage across each resistor:

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VVOLTAGE DIVIDER RULE AND CURRENT DIVIDER RULE

SERIES-PARALLEL CIRCUIT

Figure 1:RAB= 500 Figure 2:RAB= 750 Figure 3:RAB= 1.517 k

Example1 a.What is the total resistance?

b.What is the current in the circuit? c.What is the potential difference across the 30 ohm resistor? d.What is the current through the 40 ohm resistor?

a. Parallel combination: 1/40 + 1/50 = 9/200 c. Voltage, V = IR R = 200/9 = 0.23X30 = 22 = 6.92 V Total resistance = 30 + 22 = 52

b. Current. I = V/R d. across the 40 ohm resistors = 12 6.92 = 12/52 = 5.08 V = 0.23 A Current = 5.08 / 40 = 0.127 A

1.5CIRCUITSERIESSERIES-PARALLELPARALLELIT = I1 = I2 = I3 = = INVT = V1 + V2 + V3 + + VNRT = R1 + R + R3 ++ RN2IT = I1 + I2 + I3 + + INVT = V1 = V2 = V3 = = VN