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CURRENT ELECTRICITY Q.1 A. Define Electric current and its unit. Electric Current It can be defined as “the time rate of flow of charge in a conductor is called Electric Current.“ The amount of flow of charge “Q“ per unit time is called Electric Current. It is a scalar quantity. It is denoted by “ I “. Mathematically Ch arg e time Q I t Electric Current The SI unit of Electric Current is Ampere (A). Ampere It can be defined as “if one coulomb of charge flows in a conductor in one second time, then the current is said to be one Ampere.“ Q.2 A. Write a note on conventional current? Conventional Current It can be defined as “ the current due to the flow of positive charge is called conventional current.“ Before the discovery of electron the scientists thought that current is causes due to the flow of positive charge proton. But later on the scientists stated that current is causes due to the flow of positive as well as negative charge. Q.3 A. State and explain Ohm's Law? Statement A German scientist George Simon Ohm in 1826 state that “the current flows in a conductor is directly proportional to the voltage supplied across the ends of the conductor provided the temperature and Resistance of the conductor is kept constant. “ Mathematically I V V I V Cons tan t ( I ) V IR Where R is constant of proportionality and are known as resistance of the wire. Experimental verification Take a thin wire of about one meter length. Connect both ends of the wire to the positive and negative plate of the battery. The voltage across the wire is measured by voltmeter and the current in the wire is measured by ammeter. By drawing a graph between current and voltage it will give a straight line. V I Validity of Ohm's Law Ohm's Law is not valid for those conductors whose temperature does not remain constant. For examples Electric tubes, Transistors and Ionic plasma. Q.4 A. Define Electrical Resistance and its unit? Electrical resistance It is the property of a conductor by which it opposes the flow of current in the conductor. It is denoted by "R". Mathematically V R I The SI unit of electrical resistance is ohm. It is denoted by omega " ". Definition of ohm The electrical Resistance of a conductor is said to be one Ohm, if one ampere of current passes through it by having a potential difference of one volt across its ends. Mathematically 1V 1 1A Q.5 A. What is meant by specific resistance? Specific Resistance The Resistance of a conductor is said to be Specific Resistance, if the conductor have a unit cross section area and unit length. The Resistance of a conducting wire is directly proportional to the length and inversely proportional to the cross section area. Mathematically R L ----------------- (1) 1 R ----------------- (2) A Combining equation (1) and (2), we get L R A L R Constant A L A A R L Where is the constant of proportionality and it is called specific Resistance. The SI unit of specific Resistance is Ohm-meter ( m ) R Q.6 A. What is the effect of temperature on electrical resistance? Effect of temperature on Resistance The Resistance of a conductor directly depends on the temperature and initial Resistance of the conductor. Explaination Consider a conductor has an initial Resistance " R " and temperature" T ". After a temperature change " T "the Resistance of conductor becomes" R ". Mathematically R R R T Combining both equations, we get R R T R Constant R T R R T R R R R T RT Rt R 1 T Q.7 A. Define Electric circuit and its types? Electric circuit The path of the flow of Electric current is known as Electric circuit. There are two types of an Electric circuit. i-e Closed circuit A complete circuit for the flow of Electric current is called closed circuit. current can easily flow in this circuit. Open circuit An incomplete circuit for the flow of Electric current is called open circuit. current can not flow in this circuit due to a break in the circuit. Q.8 A. Write a note on series combination of Resistors? Series combination of Resistors The end to end connection of two or more than two Resistors with each other is called Series combination of the Resistors. As shown in Fig (i) (ii) Series combination has the following characteristics. There is a single path for the flow of current it means that current is constant in the circuit. Mathematically I I1 I 2 I 3 Voltage across each Resistor is drop. It means that the sum of the individual voltage is equal to the total voltage. Mathematically ----------------- (A) Veq V1 V2 V3 But according to Ohm’s law; V3 IR3 V1 IR1 , V2 IR2 , Veq IReq , Put these values in equation (A) IR eq IR1 IR 2 IR3 Req R1 R2 R3 For "n" numbers of Resistors, we have Req R1 R2 R3 Rn Q.9 A. (i) Write a note on parallel combination of Resistors? Parallel combination of Resistors The connection of two or more than two Resistors in which each and every Resistor is parallel to each other is called parallel combination of Resistors. As shown in Fig below. Parallel combination has the following characteristics. Voltage across each Resistor is constant. Mathematically V V1 V2 V3 (ii) The current flows in each Resistor is different. The sum of the individual current across the Resistors is equal to the equivalent current. Mathematically I I 1 I 2 I 3 --------- (A) But according to Ohm’s law; V I 3 R3 V I 1 R1 , V I 2 R2 , V IReq , V V V , , , I1 I2 Req R1 R2 Put these values in equation (A), we get V V V V Req R1 R2 R3 V 1 1 1 V( ) Req R R R I I3 V R3 1 1 1 1 Req R1 R2 R3 For "n" numbers of Resistors 1 1 1 1 1 Req R1 R2 R3 Rn For only two Resistors "R1" and "R2" 1 1 1 Req R1 R2 R2 R1 1 Req R1 R2 Req R1 R2 R1 R2 Q.10 What is meant by Electric Power and Electric Energy? Explain A. Electric Power The time rate of doing work is called Power. Mathematically W P ----------- (1) t The work done in electric field on a unit charge is represented by "V". So the work done on charge "Q", will be W QV Put the value of "W" in equation (1) QV P t We know that; I Q t So P IV But we also know that from Ohm’s law; V IR P I ( IR ) I 2 R Unit of Power The SI unit of Power is watt. The other units of Power are Kilowatt, Horse Power. Mathematically 1KW 1000W 1 Horse Power 746watt Electric Energy The energy produce by generators and consumed by different appliances such as Heater, fans, bulb, etc is called Electric Energy. It is denoted by "H". Mathematically Energy Power time H P t --------- (2) As we know that P I 2R Put this value of "P" in equation (2) H I 2 R t I 2 Rt Unit of Energy The different units of Energy are joule, kilowatt hour, electron volt, etc. 1KWh 3 6 106 J 1eV 1 6 1019 J Q.11 Differentiate between DC and AC? A. Direct Current D.C stands for direct current. This type of current always flow in one direction. This current flows from positive to negative terminal of the battery. Alternating current A.C stands for alternating current. This type of current changes its direction many times in a second. Alternating current changes its direction alternatively from the positive half to the negative half. Q.12 What are the main components of a circuit? A. The basic components of a circuit are as under; Switches It is an electric circuit control element with two discrete states ON and OFF. Current flows in a circuit if switch is ON, otherwise current can not flow. The symbol for a switch is “ “. Resistors The devices connected in a circuit to reduce current is called resistor. They are made from wire coil of special alloys or from carbon. The symbol for a resistor is “ “. Batteries The combination of many cells is called a battery. Battery is often made from chemical substances. The symbol for a battery is “ “. Q.13 Write note on the following instruments. i. Galvanometer ii. Ammeter iii. Voltmeter A. Galvanometer It is a sensitive device used to detect small amount of current in a circuit. It consist of a dial on which a needle can rotate. In order to detect current in the circuit galvanometer is connected in series with the circuit. The deflection of the needle indicates the presence of current in the circuit. Ammeter The device which measure current in a circuit is called Ammeter. It is a modified galvanometer for measuring large currents. This modification is accomplished by connecting a low resistance in parallel with galvanometer. This resistance is known as shunt resistance which provides an alternate path for the flow of current. To measure current Ammeter is connected in series with the circuit. Voltmeter The device which measure Voltage in a circuit is called Voltmeter. It is also a modified galvanometer in which a large resistance is connecting in series. To measure voltage across the terminals Voltmeter is connected in parallel with the circuit. Q.14 Differentiate between Series and Parallel circuits. A. Series circuit The circuit in which the current in different paths flow one after the other is called Series circuit. In case of Series circuit the voltage drops across each resistor. The total voltage is equal to the sum of individual voltage across each resistor. Mathematically V = V1 + V 2 Parallel circuit The circuit in which current flows on different path is called Parallel circuit. In case of Parallel circuit the current drop across each resistor. The total current is equal to the sum of individual current across each resistor. Mathematically I = I1 + I2 Q.15 What is electricity Hazards? A. Hazards The electricity comes to our houses by means of cable. These cables consist of two wire live wire and neutral wire. The live wire and any terminal connected to it are very dangerous. Anyone who touches a live wire would suffer a fatal shock, because human body conducts electricity. The electric shock also occurs due to damage insulation, overheating of cables and damped condition. We should not walk upon wires bare foot. Q.16 How electricity is used safely in homes? A. The electricity supplied to our homes is alternating current (A-C). It changes its direction 50 times in a second. So its frequency is 50Hz and voltage is 220V. For the safe use of electricity the following devices should be used in the house circuit. Fuse It consists of a thin piece of metal wire having low melting point. When too much current flows through the fuse wire. It melts before the copper wire in the circuit get hot. As a result the circuit breaks and no damage occur. Circuit breaker It consists of an electromagnet, when current exceeds the rated value of the circuit breaker. It automatically separates the contact of the circuit wires and breaks the circuit. Now a day it is used instead of fuse, because it works quickly than fuse. Earth wire A wire which goes to the top connection on all power sockets and is connected with the earth. This wire is a safety precaution to prevent electric shock when an appliance develops a fault. SHORT QUESTIONS 1. A. 2. A. 3. A. 4. A. 5. A. Electric current is a flow of charge, why two wires rather than a single wire is used to carry current. The electric current flow just like water in a pipe. The water flows from a higher concentration end of the pipe to the lower concentration end. Similarly electric current also flow from a higher concentration end to the lower concentration end. Therefore two wires are used rather than a single wire for the flow of current. Which solids are good electrical conductors and which are good insulators? How well do these substance conduct heat. Metallic solids are good conductor of electricity. For example copper, silver, iron etc. Non metallic solids are good insulator of electricity. For example wood, plastic, rubber etc. Basically good conductors of electricity are good conductor of heat. Therefore metallic solids conduct heat. While non metallic solids can not conduct heat. State how the resistance of a wire would change (i) if its length is increased (ii) if its diameter is decreased. The resistance of a wire depends upon the length and area of the wire. Mathematically L R A d A r 2 ( ) 2 2 4L R 2 d This equation shows that if we increase the length of the wire the resistance increases. Also if we decrease the diameter of the wire the resistance will also be increases. To reduce the brightness of a light bulb an auxiliary resistance be connected in series with it or in parallel? Why To reduce the brightness of the bulb auxiliary resistance must be connected in series. Because in series combination potential difference across the resistors decreases. As a result the brightness of bulb will be reduced. A number of light bulbs are to be connected to a single power outlet. Will they provide more illumination if connected in series or in parallel? Why To get more illumination the bulb must be connected in parallel. Because in parallel combination of the resistors voltage remain constant. As voltage reached equally to each and every bulb. Therefore the illumination will be greater. 6. What is meant by the statement that an electric kettle has power of 2KW? A. Electric kettle has a power of 2KW means that its power is 2000W. so if an operating voltage of (220 to 240volts) is applied across its heating element, then it will convert electrical energy into heat energy at the rate of 2000 j/sec. mathematically E P t E Pt E 2000W 1Sec 2000 j 7. A. 8. A. 9. A. When incandescent lamps burn out, they usually do so just after they are switched on. Why? Incandescent lamps are generally used to get heat energy using electrical energy. That is why they may burn out when switched on. Most of the electrical energy is converted into thermal energy and some produce light. Why is it possible for a bird to perch on a high voltage wire without being electrocuted? it is possible for a bird to perch on a high voltage wire without being electrocuted. Because the potential difference between the wire and the feet of the bird is zero. Why is it dangerous to turn on a light when you are in the bath tub? The human body is a good conductor of electricity. Therefore when a person in a bath tub tries to turn on a bulb, he may get on an electric shock. NUMERICAL PROBLEMS 1. A steady current of 0.5A flows through wire. How much charge passes through the wire in one minute? Given data I 0 5A t 1 min 60 sec Q? We know that Q t Q It Q 0 5 60 30C I 2. A wire carries a current of 1A. How many electrons pass at any point in the wire each second? Given data I 1A t 1sec e 1 6 10 19 C n? We know that Q ne (1) Q It (2) Comparing equation (1) and (2) we get ne It It n e 11 1 1019 0 625 1019 19 1 6 1 6 10 n 6 25 1018 electrons n 3. A 120V toaster has a resistance of 12ῼ. What must be the minimum rating of the fuse in electrical circuit to which toaster is connected? Given data V 120V R 12 I ? We know that V IR I 4. V 120 10 A R 12 An electric heater uses 5.0A when connected across 110V. Determine its resistance. Given data I 5 0A V 110V R? We know that V IR V 110 R 22 I 50 5. A metal rod is 2m long and 8mm diameter. Compute its resistance if the resistivity of the metal is 1.76 x 10-7ῼm. Given data L 2m d 8mm 8 103 m d 8 103 r 4 103 m 2 2 1 76 108 m R? We know that R L A A r 2 R L r 2 R 1 76 10 8 2 (3.14)(4 10 3 ) 2 3 52 10 8 R 3 14 16 10 6 3 52 R 10 8 10 6 50 24 R 0 070 10 8 6 R 0 070 10 2 R 7 10 4 6. A platinum wire 80cm long is to have a resistance of 0.1ῼ. What should its diameter be? The resistivity of platinum is 1.1 x 10-7ῼm. Given data L 80cm 0 8m R 0 1 1 1 10 7 m d ? We know that R L A L d ( )2 2 4L R d 2 4L d2 R R d 2 1 1 107 4(0 8) 3.14 0 1 3 52 107 0 314 2 d 11 21 107 d2 d 2 1 12 106 d 1 06 103 m 1 06mm 7. A copper wire has a resistance of 10ῼ at 20˚C. What will be the resistance at 0˚C? The temperature coefficient of resistance of copper is 0.004C-1. Given data R 10 T1 20 C T2 0 C T T2 T1 0 20 20 C 0 004C 1 R? We know that R R (1 T ) R 10(1 0 004 20) R 10(1 0 08) R 10(0 92) R 9 2 8. What is the equivalent resistance of three 5ῼ resistors connected in series? If a potential difference of 60V is applied across the combination, what is the current in each resistor? Given data R1 R2 R3 5 V 60V Req ? I1 , I 2 , I 3 ? We know that Req R1 R2 R3 Req 5 5 5 Req 5 We also know that V IR V 60 I 4A R 15 In series combination of resistors current remain constant. So I1 I 2 I 3 4 A 9. What is the equivalent resistance of three 5ῼ resistors connected in parallel? If a potential difference of 60V is applied across the combination, what is the current in each resistor? Given data R1 R2 R3 5 V 60V Req ? I1 , I 2 , I 3 ? We know that 1 1 1 1 Req R1 R2 R3 1 1 1 1 Req 5 5 5 1 111 Req 5 1 3 Req 5 Req 5 1 67 3 We also know that V IR V I R V 60 I1 12 A R1 5 10. I2 V 60 12 A R2 5 I3 V 60 12 A R3 5 An electric iron of resistance 20ῼ takes a current of 5.0A. Calculate the thermal energy, in joules, developed in 30sec. given data R 20 I 5 0A t 30Sec H ? We know that H H H H H I 2 Rt (5)(20)(30) 25 20 30 15000J 15KJ