Electromagnetism Lecture#3 Instructor: Engr. Muhammad Mateen Yaqoob

Definition of Capacitance Consider two conductors carrying charges of equal magnitude and opposite sign Such a combination of two conductors is called a capacitor. The conductors are called plates. A potential difference exists between the conductors due to the presence of the charges Experiments show that the quantity of charge Q on a capacitor is linearly proportional to the potential difference between the conductors; that is Q ∞ ⌂V MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

Definition of Capacitance Capacitance is a measure of a capacitor’s ability to store charge. Because positive and negative charges are separated in the system of two conductors in a capacitor, there is electric potential energy stored in the system The SI unit of capacitance is the farad (F) MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

Construction of Capacitor Each plate is connected to one terminal of a battery, which acts as a source of potential difference. If the capacitor is initially uncharged, the battery establishes an electric field in the connecting wires when the connections are made. Let us focus on the plate connected to the negative terminal of the battery. The electric field applies a force on electrons in the wire just outside this plate; this force causes the electrons to move onto the plate. MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

Construction of Capacitor This movement continues until the plate, the wire, and the terminal are all at the same electric potential. Once this equilibrium point is attained, a potential difference no longer exists between the terminal and the plate, and as a result no electric field is present in the wire, and the movement of electrons stops. The plate now carries a negative charge. A similar process occurs at the other capacitor plate, with electrons moving from the plate to the wire, leaving the plate positively charged. In this final configuration, the potential difference across the capacitor plates is the same as that between the terminals of the battery. MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

Capacitors with Dielectrics A dielectric is a non-conducting material, such as rubber, glass, or waxed paper. When a dielectric is inserted between the plates of a capacitor, the capacitance increases. If the dielectric completely fills the space between the plates, the capacitance increases by a dimensionless factor K, which is called the dielectric constant of the material. MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

Current (I) Electrical current is the rate of flow of charges where: I = current in amperes (A) Q = charge in coulombs (C) t = time in seconds (s) the rate of flow of charge. Random motion of free electrons in a material. Electrons flow from negative to positive when a voltage is applied across a conductive or semiconductive material. MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

Definition of Current One ampere (1 A) is the amount of current that exists when a number of electrons having a total charge of one coulomb (1 C) move through a given cross-sectional area in one second (1 s). MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

Electric Current The SI unit of current is the ampere (A), 1 A of current is equivalent to 1 C of charge passing through the surface area in 1 s. 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 is due to the motion of negatively charged electrons. Therefore, when we speak of current in an ordinary conductor, the direction of the current is opposite the direction of flow of electrons. If the ends of a conducting wire are connected to form a loop, all points on the loop are at the same electric potential, and hence the electric field is zero within and at the surface of the conductor. MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

Example MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

Resistance (R) Resistance is the opposition to current. Definition of resistance One ohm (1 Ω) of resistance exists if there is one ampere (1 A) of current in a material when one volt (1 V) is applied across the material. MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

Superconductors There is a class of metals and compounds whose resistance decreases to zero when they are below a certain temperature Tc, known as critical temperature. These materials are known as superconductors. The resistance–temperature graph for a superconductor follows that of a normal metal at temperatures above Tc. When temperature is at or below Tc, resistivity drops suddenly to zero. MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

Superconductors This phenomenon was discovered in 1911 by the Dutch physicist Heike Kamerlingh-Onnes (1853– 1926) as he worked with mercury, which is a superconductor below 4.2 K. Two kinds of superconductors are recognized. The more recently identified ones are essentially ceramics with high critical temperatures, whereas superconducting materials such as those observed by Kamerlingh-Onnes are metals. If a room-temperature superconductor is ever identified, its impact on technology could be tremendous. The value of Tc is sensitive to chemical composition, pressure, and molecular structure. It is interesting to note that copper, silver, and gold, which are excellent conductors, do not exhibit superconductivity. MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

OHM’s LAW The most important fundamental law in electronics is Ohm’s law, which relates voltage, current, and resistance. Georg Simon Ohm ( ) studied the relationship between voltage, current, and resistance and formulated the equation that bears his name. In terms of current, Ohm’s law states MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

OHM’s LAW Ohm's law states that current is directly proportional to voltage and inversely proportional to resistance. I α V Constant Resistance I α 1/R Constant Voltage where: I = current in amperes (A) V = voltage in volts (V) R = resistance in ohms (Ω) MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

The Linear Relationship of Current and Voltage In resistive circuits, current and voltage are linearly proportional. Linear means that if one of the quantities is increased or decreased by a certain percentage, the other will increase or decrease by the same percentage, assuming that the resistance is constant in value. V= 10V, V=30V MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

Example Assume that you are measuring the current in a circuit that is operating with 25 V. The ammeter reads 50 mA. Later, you notice that the current has dropped to 40 mA. Assuming that the resistance did not change, you must conclude that the voltage source has changed. How much has the voltage changed, and what is its new value? MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

CALCULATING CURRENT How many amperes of current are in the following circuit? MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

CALCULATING VOLTAGE In the circuit of following Figure, how much voltage is needed to produce 5 A of current? MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

CALCULATING VOLTAGE How much voltage will be measured across the resistor ? MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

CALCULATING RESISTANCE In the circuit of following Figure, how much resistance is needed to draw 3.08 A of current from the battery? MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

Which circuit in Figure has the most current? The least current? MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

RESISTORS IN SERIES When connected in series, resistors form a "string" in which there is only one path for current. A series circuit provides only one path for current between two points so that the current is the same through each series resistor. MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

CURRENT IN A SERIES CIRCUIT The current is the same through all points in a series circuit. MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

TOTAL SERIES RESISTANCE The total resistance of a series circuit is equal to the sum of the resistances of each individual series resistor. Total resistance increases with each additional series resistor MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

Series Resistance Formula For any number of individual resistors connected in series, the total resistance is the sum of each of the individual values. Where n= 1,2,3………………. R T = R 1 + R 2 + R Rn MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

Determine the value of R 4 in the circuit of following figure? 1OkΩ MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

The Case of Two Resistors in Parallel The total resistance for two resistors in parallel is equal to the product of the two resistors divided by the sum of the two resistors. MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

The Case of Equal-Value Resistors in Parallel MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

KIRCHHOFF'S CURRENT LAW Kirchhoff's voltage law deals with voltages in a single closed path. Kirchhoff’s current law applies to currents in multiple paths. Kirchhoff's current law, often abbreviated KCL, can be stated as follows: ‘’The sum of the currents into a node (total current in) is equal to the sum of the currents out of that node (total current out)’’. MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

KIRCHHOFF'S CURRENT LAW A node is any point or junction in a circuit where two or more components are connected. In a parallel circuit, a node or junction is a point where the parallel branches come together. Node A Node B MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

KIRCHHOFF'S VOLTAGE LAW The sum of all the voltage drops around a single closed path in a circuit is equal to the total source voltage in that loop. Vs = V 1 + V 2 + V Vn MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

Problems related to Kirchhoff's Voltage Law Q.1Five resistors are in series with a 20 V source. The voltage drops across four of the resistors are 1.5 V, 5.5 V, 3 V, and 6 V. How much voltage is dropped across the fifth resistor? MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

FIRST-ORDER CIRCUIT Three passive elements (resistors, capacitors, and inductors) individually, Circuits having various combinations of two or three of the passive elements. RC and RL circuits. Analysis of RC and RL circuits by applying Kirchhoff’s laws. The differential equations resulting from analyzing RC and RL circuits are of the first order. Hence, the circuits are collectively known as first-order circuits. MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

The natural response of a circuit refers to the behavior (in terms of voltages and currents) of the circuit itself, with no external sources of excitation. The voltage response of the RC circuit. MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

The time constant of a circuit is the time required for the response to decay by a factor of 1/e or 36.8 percent of its initial value. The voltage response of the RC circuit. MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE

Applications of RC and RL circuits RC and RL Circuits have many applications in the field of Electrical, Electronics, Communication, Computer Engineering, Signal Processing and so on These circuits have many practical applications, some of their major applications are listed below: 1.Amplifiers 2.Oscillators 3.Filters 4.Switching Regulator 5.Tuned Amplifiers 6.Radio Transmitter and Receiver 7.TV Receiver MATEEN YAQOOB DEPARTMENT OF COMPUTER SCIENCE