Electricity 1 PDF

# Class X - Science: Electricity (L1) ## PK Hits: - Ohm's Law Graph - Numerical: - Series and Parallel resistance - $R = ρ(L/A)$ - Power Heating effect ## Electric Charge: - Charge is a fundamental particle in an atom. - It may be positive or negative. Electrons carry a negative charge, and protons carry a positive charge. - Unlike charges attract each other. - Coulomb (C): S. I. unit of charge - 1 Coulomb charge = $6 × 10^{18}$ electrons ## Quantisation of Charge: - According to charge quantization, any charged particle can have a charge equal to some integral number of e. i.e., $Q = ne$, where n = $1, 2, 3,...$ - Q = net charge - n = no of electrons - e = charge on an electrons ## Electrical Substances: | Type | Description | Examples | |---|---|---| | Conductors | Allow electric current to flow easily. Contain free electrons. | Copper, aluminum. | | Semiconductors | Have electrical conductivity between conductors and insulators. Conductivity can be altered by adding impurities or changing temperature. | Silicone, germanium. | | Insulators | Do not allow electric current to flow easily. Lack free electrons. | Rubber, plastic. | ## Electric Current: - Electric current is defined as the rate of flow of charge through a cross-section of a conductor per unit time. - It is denoted by I. - SI unit: Ampere (A) or coulomb per second - $I = \dfrac{Q}{t}$ - One ampere is the current flowing through a conductor when 1 coulomb of charge flows per second. ## Potential Difference: - Electric Potential Difference: The potential difference between two points in an electric circuit is the work done to move a unit charge from one point to another. It is the driving force that causes the flow of electric current. - It is denoted by V - SI unit: Volt (V) or joule per coulomb - $V = \dfrac{W}{Q}$ - 1 volt: is the potential difference between two points when 1 joule of work is done to move 1 coulomb of charge between them. ### Example: - Q. Work of 14 J is done to move 2 C charge between two points on a conducting wire. What is the potential difference between the two points? - $V = \dfrac{W}{Q} = \dfrac{14}{2} = 7V$ ### Example: - Q. ii. A boy records that 4000 joules of work is required to transfer 10 coulombs of charge between two points of a resistor of 50 Ω. The current passing through it is: - $V = \dfrac{W}{Q} = \dfrac{4000}{10} = 400 V$ - $I = \dfrac{V}{R} = \dfrac{400}{50} = 8 A$ ## Electric Circuit: - **Electrical Circuit:** A closed path of wires and components through which electric current flows when a potential difference is applied. - **Components:** - Electric devices - Source of electricity. - Connecting wires and a switch to control the flow of current. ## Circuit Elements: | Sl. No. | Components | Symbols | |---|---|---| | 1 | An electric cell | - + | | 2 | A battery or a combination of cells | -- | | 3 | Plug key or switch (open) | -- | | 4 | Plug key or switch (closed) | -- | | 5 | A wire joint | - | | 6 | Wires crossing without joining | + | | 7 | Electric bulb | Ω or | 8 | A resistor of resistance R | -- | | 9 | Variable resistance or rheostat | -- | | 10 | Ammeter | -- | | 11 | Voltmeter | -- | ## Ammeter: - An ammeter is an instrument used to measure the electric current flowing through a circuit. - It is always connected in series with the circuit so that the entire current passes through it. - The device has very low resistance to minimize its impact on the circuit's overall current flow. - Ammeter readings are usually given in amperes (A) or milliamperes (mA). ## Voltmeter: - A voltmeter is a device used to measure the potential difference (voltage) between two points in an electric circuit. - It is connected in parallel to the section of the circuit where the voltage is to be measured. - A voltmeter has very high resistance to ensure it does not draw significant current from the circuit, maintaining accurate readings. - It is represented by V (Volts). ## Ohm's Law: - **Ohm's Law:** states that the current (I) flowing through a conductor is directly proportional to the voltage (V) across it and inversely proportional to its resistance (R). - The constant of proportionality R is called Resistance represented by the symbol Ω - $V = IR$ ## V-I Characteristic Graph: - When potential difference is 1 V, and current through the circuit is 1 A, then resistance is 1 ohm. - The graph of voltage vs current is a straight line. ## Resistance: - **Resistance:** is the property of a material that opposes the flow of electric current through it. - Its SI Unit is Ohm (Ω). - $R = \dfrac{V}{I}$ - A component that is used to resist the flow of electric current in a circuit is called a **resistor**. ## Rheostat: - A rheostat is a variable resistor used to control the current in a circuit by adjusting its resistance. - It is commonly used in devices like dimmer switches, fans, and other electrical equipment to regulate current flow. ## Factors Affecting Resistance: - Resistance of a uniform metallic conductor: - Directly proportional to the length of conductor: $R ∝ L$ - Inversely proportional to the area of cross-section: $R ∝ \dfrac{1}{A}$ - Directly proportional to the temperature: $R ∝ Temperature$ - Depends on nature of material: (p) $R = \dfrac{ρL}{A}$ ## Resistivity: - **Resistivity:** is a material's intrinsic property that measures its opposition to the flow of electric current. - It is denoted by ρ - Resistivity does not change with change in length or area of cross-section, but it changes with change in temperature. - $ρ = \dfrac{R A}{L}$ | Material | Resistivity (Ω m) | |---|---| | Silver | 1.60 × 10-8 | | Copper | 1.62 × 10-8 | | Aluminium | 2.63 × 10-8 | | Tungsten | 5.20 × 10-8 | | Nickel | 6.84 x 10-8 | | Iron | 10.0 × 10-8 | | Chromium | 12.9 × 10-8 | | Mercury | 94.0 × 10-8 | | Manganese | 1.84 × 10-6 | | Constantan (alloy of Cu and Ni) | 49 × 10-6 | | Manganin (alloy of Cu, Mn and Ni) | 44 × 10-6 | | Nichrome (alloy of Ni, Cr, Mn and Fe) | 100 × 10-6 | | Glass | 1010- 1014 | | Hard rubber | 1013-1016 | | Ebonite | 1015-1017 | | Diamond | 1012 - 1013 | | Paper (dry) | 1012 | ## Resistance vs Resistivity: | Resistance | Resistivity | |---|---| | Resistance refers to the opposition that a material offers to the flow of electric current through it. | Resistivity is a property of a material that describes how strongly it resists the flow of electric current. | | Resistivity depends on the temperature and the nature of material. | | SI unit: Ω | SI unit: Ωm | ### Example: - Which one among a bar of an alloy of mass 2 kg and a 3 kg iron bar of the same dimension has greater resistivity? - Answer: Alloy bar because it has different types of atoms. ### Example: - A resistance wire is stretched so as to double its length. Its new resistivity will have a magnitude: - Answer: Same as its original ### Example: - Q. Plastic insulation surrounds a wire having diameter d and length I as shown below. A decrease in the resistance of the wire would be produced by an increase in the: - Answer: Diameter d of the wire. Because Resistance is inversely proportional to the area, and an increase in the diameter will directly increase the area. ## Combination of Resistor in Circuit: ### Series Combination: - When two or more resistors are connected end to end, the arrangement is called series combination. - $R_{net} = Total$ - Effective resistance in series: - $R_{s}=R_{1}+R_{2}+R_{3}$ - In a series circuit, the total voltage is the sum of the voltage drops across each resistor. - In a series circuit, the same current flows through each resistor. ### Parallel Combination: - When two or more resistors are connected across multiple branches. - Effective resistance in parallel: - $1/R_{p} = 1/R_{1} + 1/R_{2} +1/R_{3}$ - In a parallel circuit, the voltage drop across each resistor is the same. - In a parallel circuit, the total current is the sum of the current flowing through each resistor. ### Examples: - Q. The image shows a combination of 4 resistors. What is the net resistance between the two points in the circuit? - The 2 Ω resistors in parallel have an equivalent resistance of R = 1 Ω. - $R = \dfrac{2\times2}{2+2} = 1 Ohms$ - This 1 Ω resistor is in series with the 3 Ω resistor, which gives a total resistance of 4 Ω. - $R_{net} = 1 + 3 = 4 Ohms$ - Q.The effective resistance between A and B is: - The 4 Ω and 6 Ω resistors are in parallel. - Because they are in parallel, the equivalent resistance is calculated as: - $R_{net} = \dfrac{4\times6}{4+6} = \dfrac{24}{10} = 2.4 Ohms$ - The 4 Ω and 6 Ω resistors can be considered as one resistor with an equivalent resistance of 2.4 Ω - Q. Two wires A and B of the same material, having the same lengths and diameters 0.2 mm and 0.3 mm respectively, are connected one by one in a circuit. Which one of these two wires will offer more resistance to the flow of current in the circuit? Justify your answer. - Wire A (0.2 mm diameter) because it has a smaller cross-sectional area compared to Wire B (0.3 mm diameter), and because resistance is inversely proportional to the area, a smaller area would mean a greater resistance. - Q. In the following figure, three cylindrical conductors A, B, and C are shown along with their lengths and areas of cross-section. If these three conductors are made of the same material and RA, RB, and R are their respective resistances, then find: - $R_{A}= \dfrac{ρL}{A}$ - $R_{B}= \dfrac{ρL}{2A} = \dfrac{1}{2} (\dfrac{ρL}{A}) = \dfrac{1}{2}R_{A}$ - $R_{C}= \dfrac{ρL}{A/2} = 2(\dfrac{ρL}{A}) = 2R_{A}$ - (i) $R_{A}/R_{B}$ - $\dfrac{R_{A}}{R_{B}} = \dfrac{R_{A}}{\dfrac{1}{2}R_{A}} = 2$ - (ii) $R_{A}/R_{C}$ - $\dfrac{R_{A}}{R_{C}}=\dfrac{R_{A}}{2R_{A}} = \dfrac{1}{2}$ - Q. The resistance of a wire of 0.01 cm radius is 10 Ω. If the resistivity of the wire is 50×10-8 Ωm, find the length of this wire. - $R= 10 Ω$ - $ρ= 50 \times 10^{-8} Ωm$ - $r = 0.01 cm$ - $A = πr^2 = π(0.01)^2 = 0.0001π cm^2$ - $l = \dfrac{RA}{ρ} = \dfrac{10 \times 0.0001π}{50 \times 10^{-8}} = \dfrac{π}{5} \times 10^4 cm = \dfrac{π}{5000} \times 10^6 m = \dfrac{π}{5} \times 1000 m = 628.3 m$ ## In the study of electric current, it is important to first understand the fundamental concept of electric charge. Electric charge is a fundamental property of matter, and it comes in two forms: positive and negative. Electrons carry a negative charge, and protons carry a positive charge. The SI unit of charge is the coulomb (C), which is equal to the amount of charge carried by 6.24 x 10^18 electrons. - Charged particles exert forces on each other. **Like charges repel each other, and unlike charges attract each other.** These forces are called **electrostatic forces**. - **Electric current** is the flow of electric charge. The SI unit of electric current is the ampere (A), which is equal to 1 coulomb of charge flowing past a point in 1 second. - **Electric potential difference** is the difference in electric potential between two points in an electric circuit. In other words, it is the amount of work required to move a unit charge from one point to another. The SI unit of electric potential difference is the volt (V). - **Resistance** is a measure of how much a material opposes the flow of electric current. The SI unit of resistance is the ohm (Ω). - **Ohm's law** states that the electric current through a conductor is proportional to the voltage applied across it and inversely proportional to the resistance of the conductor. - **Resistors** are components in electric circuits that are designed to oppose the flow of electric current. **A rheostat** is a variable resistor that allows you to control the amount of current flowing through a circuit. - **Electric circuits** are closed paths that allow electric current to flow. They consist of components such as resistors, batteries, switches, and wires. - **An ammeter** is an instrument used to measure electric current. - **A voltmeter** is an instrument used to measure electric potential difference (voltage). - Electric current can be used to do work. For example, it can be used to light a bulb, power a motor, or heat a wire. - The flow of electric current is not always beneficial. It can also cause damage. - Understanding the basics of electric current is essential for working with electrical devices.

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