Chapter 21 Circuits PDF

Chapter 21 :Circuits MRS. POOJA BRAHMAIAHCHARI Resistors in Series and Parallel Resistor that limits the flow of charge in the circuit. A measure of this limit on charge flow is called resistance. The simplest combinations of resistors are the series and...

Chapter 21 :Circuits MRS. POOJA BRAHMAIAHCHARI Resistors in Series and Parallel Resistor that limits the flow of charge in the circuit. A measure of this limit on charge flow is called resistance. The simplest combinations of resistors are the series and parallel connections illustrated in Figure. The total resistance of a combination of resistors depends on both their individual values and how they are connected. Resistors in Series Resistors are in series whenever the flow of charge, called the current, must flow through devices sequentially. let us consider the loss of electrical power, called a voltage drop, in each resistor. According to Ohms law, V = IR ; Voltage drop across resistor R1 is V1 = I R1; R2 is V2 = I R2; R3 is V3 = I R3; Therefore, total voltage across the circuit V = V1 + V2 + V3; Total or Equivalent Resistance in series Rs = R1 + R2 + R3 Resistors in Parallel Resistors in parallel, wired to a voltage source. Resistors are in parallel when each resistor is connected directly to the voltage source by connecting wires. Each resistor thus has the full voltage of the source applied to it. Since each resistor in the circuit has the full voltage, the currents flowing through the individual resistors are 𝑉 𝑉 𝑉 𝐼1 = , 𝐼2 = , 𝐼3 = ; 𝑅1 𝑅2 𝑅3 1 1 1 1 The total or equivalent resistance in parallel = + + +…., 𝑅𝑃 𝑅1 𝑅2 𝑅3 1. Two 100Ω resistors are connected a) in parallel and b) in series, to a 24.0V battery. What is the current through each resistor and what is the equivalent resistance of each circuit.?  Combinations of Series and Parallel 2. Consider the circuit shown below. A. Calculate the equivalent resistance of the circuit B. Calculate the current flowing through each resistor. C. Calculate the voltage across the circuit. D. Determine the power absorbed by each Resistor. E. Calculate the power delivered by the battery. Why do lights dim when a large appliance is switched on? The answer is that the large current the appliance motor draws causes a significant drop in the wires and reduces the voltage across the light. Electromotive Force: Terminal Voltage When you forget to turn off your car lights, they slowly dim as the battery runs down. If you connect an excessive number of 12-V lights in parallel to a car battery, they will be dim. The reason for the decrease in output voltage for depleted or overloaded batteries is that all voltage sources have two fundamental parts—a source of electrical energy and an internal resistance. Electromotive Force All such devices create a potential difference and can supply current if connected to a resistance. On the small scale, the potential difference creates an electric field that exerts force on charges, causing current. We thus use the name electromotive force, abbreviated emf.  Electromotive force is directly related to the source of potential difference. However, emf differs from the voltage output of the device when current flows. To be precise, the electromotive force (emf) is the potential difference of a source when no current is flowing. Units of emf are volts. Internal Resistance A 12-V truck battery is physically larger, contains more charge and energy, and can deliver a larger current than a 12-V motorcycle battery. Both are lead-acid batteries with identical emf, but, because of its size, the truck battery has a smaller internal resistance. Internal resistance is the inherent resistance to the flow of current within the source itself. The smaller the internal resistance for a given emf, the more current and the more power the source can supply. Terminal Voltage The voltage output of a device is measured across its terminals and, thus, is called its terminal voltage. Terminal voltage is given by, 𝑉 = 𝑒𝑚𝑓 − 𝐼𝑟 where r is the internal resistance and I is the current flowing at the time of the measurement. You can see that the larger the current, the smaller the terminal voltage. And it is likewise true that the larger the internal resistance, the smaller the terminal voltage. 3. A certain battery has a 12.0-V emf and an internal resistance of 0.100Ω. Calculate its terminal voltage when connected to a 10.0 Ω load. Multiple Voltage Sources There are two voltage sources when a battery charger is used. Voltage sources connected in series are relatively simple. When voltage sources are in series, their internal resistances add and their emfs add algebraically. The disadvantage of series connections of cells is that their internal resistances add.  Two voltage sources with identical emfs in parallel and connected to a load resistance. In this simple case, the total emf is the same as the individual emfs. But the total internal resistance is reduced, since the internal resistances are in parallel. The parallel connection thus can produce a larger current. Animals as Electrical Detectors A number of animals both produce and detect electrical signals. Fish, sharks, platypuses, and echidnas (spiny anteaters) all detect electric fields generated by nerve activity in prey. Electric eels produce their own emf through biological cells called electroplaques. Electroplaques are flat, disk-like cells; those of the electric eel have a voltage of 0.15 V across each one. Solar Cell Arrays Solar cell is an example for multiple voltage source, wired in both series and parallel combinations to yield a desired voltage and current. Photovoltaic generation (PV), the conversion of sunlight directly into electricity, is based upon the photoelectric effect. Most solar cells are made from pure silicon—either as single-crystal silicon, or as a thin film of silicon deposited upon a glass or metal backing.  Most single cells have a voltage output of about 0.5 V, while the current output is a function of the amount of sunlight upon the cell. The output of the solar cells is direct current. For most uses in a home, AC is required, so a device called an inverter must be used to convert the DC to AC. Kirchhoff’s Rules Two circuit analysis rules that can be used to analyze any circuit, simple or complex. These rules are special cases of the laws of conservation of charge and conservation of energy. The rules are known as Kirchhoff’s rules, after their inventor Gustav Kirchhoff (1824–1887). Kirchhoff’s first rule Kirchhoff’s first rule—the junction rule. The sum of all currents entering a junction must equal the sum of all currents leaving the junction. The first rule is the application of conservation of charge, 3. Calculate the current flow using kirchhoffs first law Kirchhoff’s Second Rule Kirchhoff’s second rule—the loop rule. The algebraic sum of changes in potential around any closed circuit path (loop) must be zero. The Second rule is the application of conservation of Energy. emf is the potential difference of a source when no current is flowing.  In a closed loop, whatever energy is supplied by emf must be transferred into other forms by devices in the loop, since there are no other ways in which energy can be transferred into or out of the circuit. Kirchhoff’s second rule requires 𝑒𝑚𝑓 − 𝐼𝑟 − 𝐼𝑅1 − 𝐼𝑅2 = 0. Rearranged, this is , 𝑒𝑚𝑓 = 𝐼𝑟 + 𝐼𝑅1 + 𝐼𝑅2 which means the emf equals the sum of the IR (voltage) drops in the loop.  When a resistor is traversed in the same direction as the current, the change in potential is -IR. When a resistor is traversed in the direction opposite to the current, the change in potential is IR. When an emf is traversed from - to + (the same direction it moves positive charge), the change in potential is +emf. When an emf is traversed from + to - (opposite to the direction it moves positive charge), the change in potential is - emf. 4. Consider the circuit apply Kirchhoff’s loop rule to calculate the voltage DC Voltmeters and Ammeters Voltmeters measure voltage, whereas ammeters measure current. Some of the meters in automobile dashboards, digital cameras, cell phones, and tuner-amplifiers are voltmeters or ammeters. Voltmeters are connected in parallel with whatever device’s voltage is to be measured. A parallel connection is used because objects in parallel experience the same potential difference. Voltmeter represented by symbol V.  Ammeters are connected in series with whatever device’s current is to be measured. A series connection is used because objects in series have the same current passing through them. Ammeters represented by the symbol A. Analog Meters: Galvanometers Analog meters have a needle that swivels to point at numbers on a scale. Digital meters, which have numerical readouts similar to a hand-held calculator. The heart of most analog meters is a device called a galvanometer, denoted by G. Current flow through a galvanometer, Ig, produces a proportional needle deflection.  The two crucial characteristics of a given galvanometer are its resistance and current sensitivity. Current sensitivity is the current that gives a full-scale deflection of the galvanometer’s needle, the maximum current that the instrument can measure. For example, a galvanometer with a current sensitivity of 50µA has a maximum deflection of its needle when 50µA flows through it. By connecting resistors to this galvanometer in different ways, you can use it as either a voltmeter or ammeter that can measure a broad range of voltages or currents. Galvanometer as Voltmeter Galvanometer can be used as a voltmeter by connecting it in series with a large resistance, R. The value of the resistance is determined by the maximum voltage to be measured. Suppose you want 10 V to produce a full-scale deflection of a voltmeter containing a 25Ω galvanometer with a 50µA sensitivity. Then 10 V applied to the meter must produce a current of 50µA. The total resistance must be Galvanometer as Ammeter The same galvanometer can also be made into an ammeter by placing it in parallel with a small resistance , often called the shunt resistance. Since the shunt resistance is small, most of the current passes through it, allowing an ammeter to measure currents much greater than those producing a full-scale deflection of the galvanometer. for example, an ammeter is needed that gives a full-scale deflection for 1.0 A, and contains the same 25Ω galvanometer with its 50µA sensitivity. Since R and r are in parallel, the voltage across them is the same. Null Measurements Voltmeters draw some extra current, whereas ammeters reduce current flow. Null measurements balance voltages so that there is no current flowing through the measuring device and, therefore, no alteration of the circuit being measured. Null measurements are generally more accurate but are also more complex than the use of standard voltmeters and ammeters, and they still have limits to their precision.  The Potentiometer Suppose you wish to measure the emf of a battery. The actual quantity measured is the terminal voltage V, which is related to the emf of the battery by V = emf - Ir, where I is the current that flows and r is the internal resistance of the battery. The emf could be accurately calculated if r were very accurately known, but it is usually not. If the current I could be made zero, then V = emf, and so emf could be directly measured.  A potentiometer is a null measurement device for measuring potentials (voltages). A voltage source is connected to a resistor R say, a long wire, and passes a constant current through it. There is a steady drop in potential (an IR drop) along the wire, so that a variable potential can be obtained by making contact at varying locations along the wire. (a) A voltage source connected to a long wire resistor passes a constant current through it. (b) An unknown emf Ex is connected as shown, and the point of contact along R is adjusted until the galvanometer reads zero. The segment of wire has a resistance Rx and script Ex = IRx , where I is unaffected by the connection since no current flows through the galvanometer. The unknown emf is thus proportional to the resistance of the wire segment. Resistance Measurements and the Wheatstone Bridge There is a variety of so-called ohmmeters that purport to measure resistance. What the most common ohmmeters actually do is to apply a voltage to a resistance, measure the current, and calculate the resistance using Ohm’s law. The Wheatstone bridge is a null measurement device for calculating resistance by balancing potential drops in a circuit. The device is called a bridge because the galvanometer forms a bridge between two branches. A variety of bridge devices are used to make null measurements in circuits. DC Circuits Containing Resistors and Capacitors An RC circuit is one containing a resistor R and a capacitor C. The capacitor is an electrical component that stores electric charge. (a) An RC circuit with an initially uncharged capacitor. Current flows in the direction shown (opposite of electron flow) as soon as the switch is closed. Mutual repulsion of like charges in the capacitor progressively slows the flow as the capacitor is charged, stopping the current when the capacitor is fully charged and 𝑄 = 𝐶. 𝑒𝑚𝑓  Voltage on the capacitor is initially zero and rises rapidly at first, since the initial current is a maximum. (b) A graph of voltage across the capacitor versus time, with the switch closing at time t =0 ; The voltage approaches emf asymptotically, since the closer it gets to emf the less current flows. We define 𝜏 = 𝑅𝐶 where 𝜏 (the Greek letter tau) is called the time constant for an circuit. As noted before, a small resistance allows the capacitor to charge faster. This is reasonable, since a larger current flows through a smaller resistance. It is also reasonable that the smaller the capacitor , the less time needed to charge it. Discharging a Capacitor (a) Closing the switch discharges the capacitor through the resistor. Mutual repulsion of like charges on each plate drives the current. (b) A graph of voltage across the capacitor versus time, with V = V0 at t =0. The voltage decreases exponentially, falling a fixed fraction of the way to zero in each subsequent time constant. RC circuits for timing RC circuits are commonly used for timing purposes. RC circuit is found in novelty jewelry, Halloween costumes, and various toys that have battery-powered flashing lights. A more crucial use of RC circuits for timing purposes is in the artificial pacemaker, used to control heart rate. The artificial pacemaker is inserted near the heart to provide electrical signals to the heart when needed with the appropriate time constant. Pacemakers have sensors that detect body motion and breathing to increase the heart rate during exercise to meet the body’s increased needs for blood and oxygen. 5. The timing device in an automobiles intermittent wiper system is based on RC time constant of 2.00s and utilizes 0.50 µF capacitor. Calculate the resistance of the circuit. THANK YOU