BIT1150 Topic Two - Voltage, Current, and Resistance PDF

2.1 Voltage Voltage, often referred to as electric potential difference, is a fundamental concept in the field of electricity and electronics. It is a measure of the electrical potential energy per unit charge at a specific point in an electrical circuit. Voltage is a key factor that drives the flo...

2.1 Voltage Voltage, often referred to as electric potential difference, is a fundamental concept in the field of electricity and electronics. It is a measure of the electrical potential energy per unit charge at a specific point in an electrical circuit. Voltage is a key factor that drives the flow of electric current through conductors and components. The unit of voltage is the "volt," which is abbreviated as "V." One volt is defined as the potential difference that will impart one joule of energy to one coulomb of charge. Voltages can be positive, negative, or zero, depending on their relative electric potential compared to a reference point (usually called the ground). Voltage is responsible for initiating and maintaining the flow of electric current. It acts as a driving force that pushes or pulls charged particles (usually electrons) through conductors and components. In a closed electrical circuit, voltage sources, such as batteries or power supplies, provide a consistent potential difference between their terminals. Voltages in electrical circuits are measured using a voltmeter, which is typically connected in parallel across the points where the voltage is to be measured. Voltage is related to current (1) and resistance (R) through Ohm’s law which states that V = I * R. Types of Voltage Voltage is divided into Direct Current (DC) and Alternating Current (AC) voltage DC Voltage: Direct Current (DC) voltage is constant and does not change over time. Batteries and most electronic devices operate on DC voltage. AC Voltage: Alternating Current (AC) voltage changes direction periodically. It is commonly used in household electricity and is generated by power stations. Safety Considerations High voltages can be dangerous and pose electrical hazards. Safety measures, such as insulation, grounding, and protective devices (e.g., circuit breakers), are used to mitigate risks associated with high voltage. 2.2 Current Current, in the context of electricity and electronics, refers to the rate of flow of electric charge through a conductor or circuit over time. It represents the movement of charged particles, typically electrons, through a medium. The symbol for current is "I." and unit of current is the "ampere," abbreviated as "A." One ampere is equivalent to one coulomb of electric charge passing through a conductor per second. Direction of Current flow Electron flow, which is the actual movement of negatively charged electrons, occurs from the negative to the positive terminal. Nature of Current Current can be either direct current (DC) or alternating current (AC) dc: Direct current flows steadily in one direction, with a constant magnitude. Batteries and most electronic devices use DC. ac: Alternating current reverses direction periodically, typically in a sinusoidal waveform. It is commonly used in household electricity and is generated by power stations. Current is measured in amperes using an ammeter. The ammeter is connected in series within the circuit to measure the current passing through a specific component or point. Current (I) is mathematically related to resistance (R) and voltage (V) through Ohm’s law which states that I = V / R. Safety Considerations High currents can pose safety hazards and can lead to electrical shocks, burns, or fire. Safety measures such as circuit protection devices (e.g., fuses and circuit breakers) are used to prevent excessive current flow. Applications Current is essential in powering electronic devices, electrical appliances, lighting systems, and electric motors. 2.3 Resistance Materials in general have a characteristic behavior of resisting the flow of electric charge. This physical property, or ability to resist current, is known as resistance and is represented by the symbol R. The unit of measurement is the "ohm," abbreviated as "Ω." One ohm is defined as the amount of resistance that allows one ampere of current to flow through a conductor when one volt of voltage is applied across it (Ω = V / I). Factors Affecting Resistance of a material Type of material: Different materials have different resistivities, which determine their resistance. For example, metals generally have low resistivity and are good conductors, while insulators have high resistivity. Length: Resistance is directly proportional to the length of the conductor. Longer conductors have higher resistance. Cross-Sectional Area: Resistance is inversely proportional to the cross-sectional area of the conductor. Larger cross- sectional areas result in lower resistance. Temperature: Resistance can change with temperature, especially for semiconductors and thermistors. In most conductors, resistance increases with higher temperatures. Resistance is mathematically related to voltage and current through Ohms Law R=V/I Resistors are often color-coded to indicate their resistance value and tolerance. The color bands on a resistor's body provide information about its resistance in ohms. Types of Resistors - Fixed Resistors: Have a constant resistance value and are used in a variety of electronic circuits. - Variable Resistors (Potentiometers): Allow the user to adjust resistance manually, often for control purposes. - Thermistors: Resistors whose resistance changes significantly with temperature. - Light-Dependent Resistors (LDRs): Change resistance based on the intensity of incident light. Applications Resistors are used in electrical circuits for various purposes, including current limiting, voltage division, signal conditioning, and temperature sensing. They are commonly used in electronic devices, such as amplifiers, filters, and voltage dividers. Ohms law and its application in electronic circuits Ohm's Law is a fundamental principle in electrical engineering and electronics that describes the relationship between voltage (V), current (I), and resistance (R) in an electrical circuit. It was formulated by the German physicist Georg Simon Ohm in the early 19th century. Ohm’s law states that the voltage v across a resistor is directly proportional to the current i flowing through the resistor. That is, v∝i Ohm defined the constant of proportionality for a resistor to be the resistance, R. (The resistance is a material property which can change if the internal or external conditions of the element are altered, e.g., if there are changes in the temperature.) Ohm's Law is often written as: V=I*R Where: - V represents voltage (measured in volts, V). - I represents current (measured in amperes, A). - R represents resistance (measured in ohms, Ω). Since the value of R can range from zero to infinity, it is important that we consider the two extreme possible values of R. An element with R = 0 is called a short circuit, For a short circuit, v = iR = 0 showing that the voltage is zero but the current could be anything. In practice, a short circuit is usually a connecting wire assumed to be a perfect conductor. Thus, A short circuit is a circuit element with resistance approaching zero. An open circuit is a circuit element with resistance approaching infinity. Example: An electric iron draws 2 A at 120 V. Find its resistance. From Ohm’s law, R = v / I = 120 / 2 = 60 Ω Exercise: The essential component of a toaster is an electrical element (a resistor) that converts electrical energy to heat energy. How much current is drawn by a toaster with resistance 12 Ω at 110 V? Resistors in Series and parallel Basically, a resistor limits the flow of charge in a circuit and is an ohmic device where V=IR. Most circuits have more than one resistor. If several resistors are connected together and connected to a battery, the current supplied by the battery depends on the equivalent resistance of the circuit. The equivalent resistance of a combination of resistors depends on both their individual values and how they are connected. The simplest combinations of resistors are series and parallel connections In a series circuit, the output current of the first resistor flows into the input of the second resistor; therefore, the current is the same in each resistor. In a parallel circuit, all of the resistor leads on one side of the resistors are connected together and all the leads on the other side are connected together. In the case of a parallel configuration, each resistor has the same potential drop across it, and the currents through each resistor may be different, depending on the resistor. The sum of the individual currents equals the current that flows into the parallel connections. Resistors in Series Resistors are said to be in series whenever the current flows through the resistors sequentially. Consider the Figure below, which shows three resistors in series with an applied voltage equal to Vab. Since there is only one path for the charges to flow through, the current is the same through each resistor. The equivalent resistance of a set of resistors in a series connection is equal to the algebraic sum of the individual resistances. (a) Three resistors connected in series to a voltage source. (b) The original circuit is reduced to an equivalent resistance and a voltage source. The current coming from the voltage source flows through each resistor, so the current through each resistor is the same. The current through the circuit depends on the voltage supplied by the voltage source and the resistance of the resistors. For each resistor, a potential drop occurs that is equal to the loss of electric potential energy as a current travels through each resistor. According to Ohm’s law, the potential drop V across a resistor when a current flows through it is calculated using the equation V=IR, where I is the current in amps ( A ) and R is the resistance in ohms (Ω). Equivalent Resistance in Series Circuits Any number of resistors can be connected in series. If N resistors are connected in series, the equivalent resistance is RS=R1+R2+R3+...+RN. One result of components connected in a series circuit is that if something happens to one component, it affects all the other components. For example, if several lamps are connected in series and one bulb burns out, all the other lamps go dark. Summary  In a series resistor circuit, resistors are connected end-to-end, forming a single path for current to flow.  The same current flows through all the resistors in the series because there is only one path for current.  The voltage across the resistors adds up. The total voltage across the series circuit is the sum of the individual voltage drops across each resistor.  The total resistance in a series circuit is the sum of the individual resistances. Mathematically, if you have resistors R1, R2, R3,..., Rn in series, the total resistance (R_total) is calculated as:  R_total = R1 + R2 + R3 +... + Rn  If one resistor fails, the entire circuit is interrupted, and no current flows. Example: Equivalent Resistance, Current, and Power in a Series Circuit A battery with a terminal voltage of 9 V is connected to a circuit consisting of four 20Ω and one 10Ω resistors all in series. Calculate the equivalent resistance of the circuit. Calculate the current through each resistor. Calculate the potential drop across each resistor. The figure shows four resistors of 20 Ω and one resistor of 10 Ω connected in series to a 9 V voltage source. Strategy In a series circuit, the equivalent resistance is the algebraic sum of the resistances. The current through the circuit can be found from Ohm’s law and is equal to the voltage divided by the equivalent resistance. The potential drop across each resistor can be found using Ohm’s law. Solution The equivalent resistance is the algebraic sum of the resistances RS=R1+R2+R3+R4+R5=20Ω+20Ω+20Ω+20Ω+10Ω=90Ω. The current through the circuit is the same for each resistor in a series circuit and is equal to the applied voltage divided by the equivalent resistance: I = V / RS = 9V / 90Ω = 0.1A. Note that the sum of the potential drops across each resistor is equal to the voltage supplied by the battery. Resistors in Parallel Resistors are in parallel when one end of all the resistors are connected by a continuous wire and the other end of all the resistors are also connected to one another through a continuous wire. The potential drop across each resistor is the same. Current through each resistor can be found using Ohm’s Law I=V/R , where the voltage is constant across each resistor. For example, an automobile’s headlights, radio, and other systems are wired in parallel, so that each subsystem utilizes the full voltage of the source and can operate completely independently. The same is true of the wiring in your house or any building. Part (a) shows original circuit with two resistors connected in parallel to a voltage source and part (b) shows the equivalent circuit with one equivalent resistor connected to the voltage source Equivalent Resistance in Parallel Circuits Generalizing to any number of N resistors, the equivalent resistance RP of a parallel connection is related to the individual resistances by RP = (1/R1+1/R2+1R3+…..+1RN) This relationship results in an equivalent resistance R P that is less than the smallest of the individual resistances. When resistors are connected in parallel, more current flows from the source than would flow for any of them individually, so the total resistance is lower. Summary In a parallel resistor circuit, resistors are connected across the same two points, creating multiple paths for current to flow. Each resistor has its own current flowing through it. The total current entering a parallel circuit is the sum of the individual branch currents. The voltage across all resistors in parallel is the same and equal to the voltage across the circuit's terminals. The total resistance in a parallel circuit is less than the smallest individual resistance. Mathematically, if you have resistors R1, R2, R3,..., Rn in parallel, the total resistance (R_total) is calculated as: 1 / R_total = (1 / R1 + 1 / R2 + 1 / R3 +... + 1 / Rn) Each resistor in parallel operates independently, and a failure in one branch does not affect the operation of other branches. Parallel resistor circuits are often used when it's essential to maintain a constant voltage across components. Example: Analysis of a parallel circuit Three resistors R1=1.00Ω, R2=2.00Ω, and R3=2.00Ω, are connected in parallel. The parallel connection is attached to a V=3.00V voltage source.  What is the equivalent resistance?  Find the current supplied by the source to the parallel circuit.  Calculate the currents in each resistor and show that these add together to equal the current output of the source. Solution The total resistance for a parallel combination of resistors RP = (1/R1+1/R2+1/R3)−1 = (1/1.00Ω+1/2.00Ω+1/2.00Ω)−1 = 0.50Ω. The total resistance with the correct number of significant digits is R eq=0.50Ω RP is less than the smallest individual resistance. The total current can be found from Ohm’s law, substituting R P for the total resistance. This gives I = V/RP = 3.00V/0.50Ω = 6.00A. Current I for each device is much larger than for the same devices connected in series. A circuit with parallel connections has a smaller total resistance than the resistors connected in series. The individual currents are easily calculated from Ohm’s law, since each resistor gets the full voltage. Thus, I1=V/R1= 3.00V/1.00Ω =3.00A. Similarly, I2=V/R2= 3.00V/2.00Ω =1.50A and I3=V/R3= 3.00V/2.00Ω =1.50A. The total current is the sum of the individual currents: I1+I2+I3=6.00A.