Physics BAS-101 Past Paper 2024-2025 - PDF

Physics BAS-101 First Level Fall Semester 2024-2025 1 By Ass. Prof. M...

Physics BAS-101 First Level Fall Semester 2024-2025 1 By Ass. Prof. Mohamed Abdelghany Dr. Nermin Ali Abdelhakim Dr. Enas lotfy Faculty of AI , Level 1, Physics, Lecture 2  2 Foundations of Electricity Faculty of AI , Level 1, Physics, Lecture 2  3 Faculty of AI , Level 1, Physics, Lecture 2  Properties of Electrical Charges 4 ❖ Every object contains a vast amount of electric charge. ❖ Electric charge can be either positive or negative. Charges with the same electrical sign repel each other, and charges with opposite electrical signs attract each other. Faculty of AI , Level 1, Physics, Lecture 2  5 ❖ An object with equal amounts of the two kinds of charge is electrically neutral, whereas one with an imbalance is electrically charged or net charged. Faculty of AI , Level 1, Physics, Lecture 2  6 Charged objects interacts by exerting forces on one another (by transformation of charge from one object to another). Faculty of AI , Level 1, Physics, Lecture 2  7 So, when a glass rod is rubbed with silk, the glass losses some of its negative (electrons) charge and then has a unbalanced positive charge And when the plastic rod is rubbed with fur, the plastic gains a unbalanced negative charge (electron). Faculty of AI , Level 1, Physics, Lecture 2  CONDUCTORS AND INSULATORS 8 Material can be classified according to the ability of charge to move through them. Materials classified to: 1. Conductor: materials through which charges can move freely, such as metal. 2. Insulators: materials in which charges cannot move freely, such as rubber, plastic, glass. 3. Semiconductors: materials that are intermediate between conductors and insulator, such as silicon, germanium. 4. Superconductors: materials that are perfect conductors where charge move without any resistance. Faculty of AI , Level 1, Physics, Lecture 2  CURRENT AND RESISTANCE 9 We study the flow of electric charges through a piece of material. The amount of flow depends on both the material through which the charges are passing and the potential difference across the material. Whenever there is a net flow of charge through some region, an electric current is said to exist. Faculty of AI , Level 1, Physics, Lecture 2 10 To define current more precisely, suppose charges are moving perpendicular to a surface of area A as shown in Figure. Faculty of AI , Level 1, Physics, Lecture 2  11 ❖The current is defined as the rate at which charge flows through this surface. ❖If ∆Q is the amount of charge that passes through this surface in a time interval ∆t, the average current Iavg is equal to the charge that passes through A per unit time: ∆𝑸 𝑰𝒂𝒗𝒈 = ∆ • Faculty of AI , Level 1, Physics, Lecture 2  12 If the rate at which charge flows varies in time, the current varies in time; we define the instantaneous current I as the differential limit of average current as ∆t → 0: …𝑸 𝑰𝒊  ” •. = … • ❑The SI unit of current is the ampere (A): 1 A = 1 C/s. That is, 1 A of current is equivalent to 1 C of charge passing through a surface in 1 s. Faculty of AI , Level 1, Physics, Lecture 2 13 ❑ It is conventional to assign to the current the same direction as the flow of positive charge. ❑ In electrical conductors such as copper or aluminum, the current results from the motion of negatively charged electrons. ❑ Therefore, in an ordinary conductor, the direction of the current is opposite the direction of flow of electrons. Faculty of AI , Level 1, Physics, Lecture 2  14 ▪ Consider the current in a cylindrical conductor of cross-sectional area A. ▪ The volume of a segment of the conductor of length ∆x (between the two circular cross sections shown in Figure, is (A ∆x). ▪ If n represents the number of mobile charge carriers per unit volume (in other words, the charge carrier density), ▪ the number of carriers in the segment is:(nA ∆x). Therefore, the total charge ∆Q in this segment is: ▪ ∆Q=(nA ∆x) q ▪ where q is the charge on each carrier. Faculty of AI , Level 1, Physics, Lecture 2  15 If the carriers move with a velocity vd (drift velocity) parallel to the axis of the cylinder, the magnitude of the displacement they experience in the x direction in a time interval ∆t is ∆x = vd ∆t. we can write ∆Q as: ∆𝑸 = 𝑨𝒗 … ∆ • 𝒒 Dividing both sides of this equation by ∆t, we find that the average current in the conductor is: ∆𝑸 𝑰𝒂𝒗𝒈 = = 𝒒𝒗 … 𝑨 ∆ • Faculty of AI , Level 1, Physics, Lecture 2  CURRENT DENISTY 16 Sometimes we are interested in the current i in a particular conductor. At other times we take a localized view and study the flow of charge through a cross section of the conductor at a particular point. To describe this flow, we can use the current density J, which has the same direction as the velocity of the moving charges if they are positive and the opposite direction if they are negative. Faculty of AI , Level 1, Physics, Lecture 2  17 Consider a conductor of cross-sectional area A carrying a current I. The current density J in the conductor is defined as the current per unit area. Because the current I = nqvdA, the current density is: 𝑰 q = = 𝒒𝒗 … 𝑨 Where A is the total area of the surface. So, we see that the SI unit for current density is the ampere per square meter (A/ m2). Faculty of AI , Level 1, Physics, Lecture 2  Now, it is possible to rewrite the draft velocity as in the form: 18 𝐢 𝐉 𝐯𝐝 = = 𝐧𝐀𝐪 𝐧𝐪 where J has SI units of amperes per meter squared. This expression is valid only if the current density is uniform and only if the surface of cross-sectional area A is perpendicular to the direction of the current. In some materials, the current density is proportional to the electric field: q = 𝝈𝑬 where the constant of proportionality σ is called the conductivity of the conductor. Faculty of AI , Level 1, Physics, Lecture 2  OHM'S LAW 19 ❑ We can obtain an equation useful in practical applications by considering a segment of straight wire of uniform cross- sectional area A and length ℓ, as shown in Figure. ❑ A potential difference ∆V = Vb - Va is maintained across the wire, creating in the wire an electric field and a current. ❑ If the field is assumed to be uniform, the potential difference is related to the field through: ∆V=Eℓ. Faculty of AI , Level 1, Physics, Lecture 2  20 Therefore, we can express the current density in the wire as: ∆𝑽 q = 𝝈𝑬 = 𝝈 𝓵 𝑰 Because q = , the potential difference across the wire is: 𝑨 𝓵 𝓵 ∆𝑽 = q = 𝑰 = y𝑰 𝝈 𝝈𝑨 𝓵 The quantity y = is called the resistance of the conductor. 𝝈𝑨 Faculty of AI , Level 1, Physics, Lecture 2  21 We define the resistance as the ratio of the potential difference across a conductor to the current in the conductor: ∆𝑽 y = 𝑰 This result shows that resistance has SI units of volts per ampere. One volt per ampere is defined to be one ohm (𝜴): Ï 𝜴 = Ï𝑽/𝑨 The inverse of conductivity is resistivity ρ: ρ= 1/σ where ρ has the units (ohm. meters) (Ω/ m). Faculty of AI , Level 1, Physics, Lecture 2  22 𝓵 Because y = , we can express the resistance of a uniform 𝝈𝑨 block of material along the length, as: 𝓵 y = F 𝑨 ✓ Every ohmic material has a characteristic resistivity that depends on the properties of the material and on temperature. ✓ In addition, the resistance of a sample depends on geometry as well as on resistivity. Faculty of AI , Level 1, Physics, Lecture 2  COULOMB’S LAW 23 The force of repulsion or attraction between two pair charges (q1 and q2) separated by a distance ( r ) from each other is given by: 𝒒 Ï 𝒒 Ð Ï 𝒒 Ï 𝒒 Ð ഥ = r † m = “ Ð Ò𝝅𝜺  “ Ð Faculty of AI , Level 1, Physics, Lecture 2  24 Ï 𝒎 Ð Where r † : is constant equal = = 𝟖. × × 𝒙 Ï𝟎 × 𝑵. Ð Ò𝝅𝜺  𝒄 𝜺  = 𝟖. 𝟖 Ó × Ï𝟎 𝒄 /𝑵. 𝒎 Ð Ï Ð Ð and 𝑞1 𝑎𝑛𝑑 𝑞2 is the charges in coulomb unit c. If we have (n) charged particle they interact independently in pairs, and the force on any one of them is given by: m Ï  † • = m Ï Ð + m Ï Ñ + m Ï Ò + ⋯ + m Ï  Faculty of AI , Level 1, Physics, Lecture 2  Charge is quantized and conserved 25 Electrical fluid is not continuous but is made up of multiples of certain elementary charge, where any charge (+ or -) can be detected and written in the form: 𝒒 =  † , where n= ±1, ±2, … and e = 1.602x10-19 C. When a physical quantity, such as charge, can have only discrete values, we say that this quantity is quantized. Also, electric charge is conserved, where the net charge of any isolated system cannot change. This means that charges not created but only transfers from one body to another. Faculty of AI , Level 1, Physics, Lecture 2  ELECTRIC FIELD 26 While we need two charges to quantify the electric force, we define the electric field for any single charge distribution to describe its effect on other charges. In principle, we can define the electric field at some point near the charged object, such as point P. We first place a positive charge qo called a test charge, at the point. We then measure the electrostatic force F that acts on the test charge. Faculty of AI , Level 1, Physics, Lecture 2  27 Finally, we define the electric field E at point P due to the charged object as: ഥ m ഥ= 𝑬 𝒒  This equation gives us the force on a charged particle qo placed in an electric field. If q is positive, the force is in the same direction as the field. If q is negative, the force and the field are in opposite directions. Faculty of AI , Level 1, Physics, Lecture 2 28 Faculty of AI , Level 1, Physics, Lecture 2 29 Faculty of AI , Level 1, Physics, Lecture 2 30  Physics BAS-101 First Level Fall Semester 2024-2025 1 By Ass. Prof. Mohamed Abdelghany Dr. Nermin Ali Abdelhakim Dr. Enas lotfy Faculty of AI , Level 1, Physics, Lecture 3  2 Foundations of Electricity Faculty of AI , Level 1, Physics, Lecture 3  Electric Field lines 3 ❑ It is an imaginary line through the space around the charge. ❑ The relation between the field lines and electric field vectors are: At any point, the direction of a straight field line or the direction of the tangent to a curved field line gives the direction of E at that point  4 The field lines are drawn so that the number of lines per unit area, measured in a plane that is perpendicular to the lines, is proportional to the magnitude of E. Thus, E is large where field lines are close together and small where they are far apart. 5 ❑ Electric field lines extend away from positive charge (where they originate) and toward negative charge (where they terminate). The rules for drawing electric field lines are as follows: 6 ❖ The lines must begin on a positive charge and terminate on a negative charge. ❖ In the case of an excess of one type of charge, some lines will begin or end infinitely far away. ❖ The number of lines drawn leaving a positive charge. ❖ Approaching a negative charge is proportional to the magnitude of the charge. ❖ No two field lines can cross.  7 Because the charges are of equal magnitude, the number of lines that begin at the positive charge must equal the number that terminate at the negative charge. At points very near the charges, the lines are nearly radial, as for a single isolated charge. The high density of lines between the charges indicates a region of strong electric field.  The Electric Field Due to a Finite Number of Point Charge 8 9 The electric field at point P due to a group of source charges can be expressed as the vector sum 𝑞𝑖 𝐸ത = 𝐾𝑒 ෍ 2 𝑟𝑖 𝑖 where ri is the distance from the ith source charge qi to the point P. 10 ❖ If a charge Q is uniformly distributed throughout a volume V, the volume charge density 𝝆 is defined by: 𝑸 𝝆= 𝑽 where ρ has units of coulombs per cubic meter (C/m3). ❖ If a charge Q is uniformly distributed on a surface of area A, the surface charge density s (Greek letter sigma) is defined by: 𝑸 𝝈= 𝑨 Where σ has units of coulombs per square meter (C/m2).  11 ❖ If a charge Q is uniformly distributed along a line of length, the linear charge density l is defined by: 𝐐 𝛌= 𝐥 where 𝝀 has units of coulombs per meter (C/m).  Flux of an Electric Field 12 ❖ Consider an electric field that is uniform in both magnitude and direction as shown in Figure. ❖ The field lines penetrate a rectangular surface of area A, whose plane is oriented perpendicular to the field.  13 ❖ The number of lines per unit area (in other words, the line density) is proportional to the magnitude of the electric field. ❖ Therefore, the total number of lines penetrating the surface is proportional to the product EA. ❖ This product of the magnitude of the electric field E and surface area A perpendicular to the field is called the electric flux Ф𝑬 :  14 ❖ The value of ∆ФE depends both on the field pattern and on the Surface. ❖ By using the integration over a closed surface, we can write the net flux ∆ФE through a closed surface as: ❖ where En represents the component of the electric field normal to the surface.  Gauss's Law 15 In this section we describe a general relationship between the net electric flux through a closed surface (often called a gaussian surface) and the charge enclosed by the surface. This relationship, known as Gauss’s law. 16 ❖ Consider a point charge q surrounded by a closed surface of arbitrary shape. ❖ The total electric flux through this surface can be obtained by evaluating E.∆A for each small area element ∆A and summing over all elements. 17 18 ❖ The electric flux is independent of the shape of the closed surface and independent of the position of the charge within the surface. 19 20 21 22  Physics BAS-101 First Level Fall Semester 2024-2025 1 By Ass. Prof. Mohamed Abdelghany Dr. Nermin Ali Abdelhakim Dr. Enas lotfy Faculty of AI , Level 1, Physics, Lecture 4  2 Foundations of Electricity Faculty of AI , Level 1, Physics, Lecture 4 3 Capacitance The basic elements of any capacitor are two isolated conductors of any shape. 4 ❑ The corresponding figure shows a less general but more conventional arrangement, called a parallel-plate capacitor, consisting of two parallel conducting plates of area A separated by a distance d. ❑ When a capacitor is charged, its plates have charges of equal magnitudes but opposite signs: +q and -q. 5 Because the plates are conductors, they are equipotential surfaces and all points on a plate are at the same electric potential. Moreover, there is a potential difference between the two plates V. 6 ❑ The charge q and the potential difference V for a capacitor are proportional to each other; that is, q= CV ❑ The proportionality constant C is called the capacitance of the capacitor. ❑ Its value depends only on the geometry of the plates and not on their charge or potential difference.  7 The capacitance is a measure of how much charge must be put on the plates to produce a certain potential difference between them.  8 ❖ The greater the capacitance, the more charge is required. ❖ The SI unit of capacitance is the coulomb per volt. This unit occurs so often that it is given a special name, the farad (F): 1 farad= 1 F = 1 coloumb / volt = 1 C/V The farad is a very large unit. Submultiples of the farad, such as the microfarad (1 μF = 10-6 F) and the picofarad (1 pF = 10-12 F), are more convenient units in practice. 9 10 11 12 13 14  Capacitor with a Dielectric 15 A dielectric is a nonconducting material such as rubber, glass, or waxed paper.  16 We can perform the following experiment to illustrate the effect of a dielectric in a capacitor. Consider a parallel-plate capacitor that without a dielectric has a charge Q0 and a capacitance C0. The potential difference across the capacitor is ∆V0= Q0/C0 17 ✓ Notice that no battery is shown in the figure; also, we must assume no charge can flow through an ideal voltmeter. ✓ Hence, there is no path by which charge can flow and alter the charge on the capacitor. ✓ If a dielectric is now inserted between the plates as in Figure, the voltmeter indicates that the voltage between the plates decreases to a value ∆V. ∆V= ∆V0 /k Because ∆V < ∆V0, we see that k > 1. ✓ The dimensionless factor k is called the dielectric constant of the material. 18 19 ❑ That is, the capacitance increases by the factor k when the dielectric completely fills the region between the plates. ❑ Because C0= Є0A/d for a parallel-plate capacitor, we can express the capacitance of a parallel-plate capacitor filled with a dielectric as: ❑ It would appear that the capacitance could be made very large by inserting a dielectric between the plates and decreasing d.  Therefore, a dielectric provides the following 20 advantages: ✓ An increase in capacitance ✓ An increase in maximum operating voltage ✓ Possible mechanical support between the plates, which allows the plates to be close together without touching, thereby decreasing d and increasing C. 21 22  Physics BAS-101 First Level Fall Semester 2024-2025 1 By Ass. Prof. Mohamed Abdelghany Dr. Nermin Ali Abdelhakim Dr. Enas lotfy Faculty of AI , Level 1, Physics, Lecture 5  2 Foundations of Electricity Faculty of AI , Level 1, Physics, Lecture 5  LAWS OF CIRCUIT THEORY 3 ❖ Basic concepts such as current, voltage, and power in an electric circuit. ❖ To actually determine the values of these variables in a given circuit requires that we understand some fundamental laws that govern electric circuits. ❖ These laws, known as Ohm’s law and Kirchhoff’s laws, form the foundation upon which electric circuit analysis is built. 4 Ohm’s Law  Nodes, Branches, and Loops 5 ❖ To differentiate between a circuit and a network. ❖ We may regard a network as an interconnection of elements or devices, whereas a circuit is a network providing one or more closed paths. ❖ In network topology, we study the properties relating to the placement of elements in the network and the geometric configuration of the network. 6 ❖Such elements include branches, nodes, and loops. 7  Kirchhoff’s Laws 8 ❖ Kirchhoff’s laws were first introduced in 1847 by the German physicist Gustav Robert Kirchhoff (1824–1887). ❖ These laws are formally known as Kirchhoff’s current law (KCL) and Kirchhoff’s voltage law (KVL). ❖ Kirchhoff’s first law is based on the law of conservation of charge, which requires that the algebraic sum of charges within a system cannot change. 9 10 11 Kirchhoff’s First Law or Kirchhoff’s Current Law 12 Kirchhoff’s second Law or Kirchhoff’s Voltage Law 13 14  Series Resistors and Voltage Division 15 ❖ Two resistors are in series, since the same current i flows in both of them. Applying Ohm’s law to each of the resistors, we obtain 16 17 Notice that the source voltage v is divided among the resistors in direct proportion to their resistances. The larger the resistance, the larger the voltage drop. This is called the principle of voltage division and the circuit in Fig. is called a voltage divider. In general  Parallel Resistors and Current Division 18 ❖ Consider the circuit in Fig., where two resistors are connected in parallel and therefore have the same voltage across them. ❖ From Ohm’s law, 19 20 ❑ The general case of a circuit with N resistors in parallel. The equivalent resistance is 21 22 23