Topic 5.1: Electric Current ~3 hours Electric Current • An electric current is a movement of electric charge that can occur in solids, liquids and gases. A steady current can be maintained when there is a drift of charge-carriers between two points of different electric potential. The charges responsible for the drift are: • Solids – electrons in metals and graphite, and holes in semiconductors • Liquids – positive and negative ions in molten and aqueous electrolytes • Gases – electrons and positive ions stripped from gaseous molecules by large potential differences. Electric Current • At this point, we will define the electric current as the rate at which charge flows past a given cross-section. q I t or dq I dt • It makes sense that for an electric current to flow, there must be a complete circuit for it to flow through. The unit of current from the above equation is the coulomb per second C s-1 and this unit is called the ampere (A). • The ampere or ‘amp’ is a rather large unit. Current is often expressed in milliamps (mA) and microamps (μA) or even nanoamps and picoamps. • When a current flows in the same direction around an electric circuit, the current is said to be a direct current (DC). Dry cell and wet cell batteries supply dc. When the direction of the current changes with time it is said to be an alternating current (AC). Household electrical (nonelectronic) appliances are AC. Current Conventions • Current is a scalar quantity but it is useful to indicate the direction of flow of current. • Before the electron was discovered, the direction of the charge-carriers was already defined by scientists and engineers to be from positive to negative. • Benjamin Franklin stated that an excess of fluid produced one kind of electric charge which he termed “positive”, and a lack of the same fluid produced the other type of electric charge which he called “negative”. Franklin’s designation of (+) being an excess of electric charge and of (–) being a deficiency of electric charge was unfortunate. • When batteries and generators, the first source of continuous current, were developed in the 1800s, it was assumed that electric current represented the flow of positive charge as defined by Franklin. This is partly the reason that electric fields are defined in terms of a positive test charge, and the lines of electric flux being explained as going outwards from positive charges. • It is now known that an electric current is a flow of electrons from negative to positive. • Unfortunately, this convention has been kept. The above figure shows a simple circuit diagram of a 1.5 V dry cell connected to a resistor. When drawing and interpreting circuit diagrams just remember that conventional current flows from the positive to negative terminal unless you are specifically asked for the correct electron flow that flows from the negative to the positive terminal. Conservation of Charge • Two devices connected in series will take the same current. • The total current entering a junction equals the total current leaving it. Electric Resistance • Electrical resistance, R, is a measure of how easily charge flows in a material. • The electric resistance of a conductor (for example, a wire of a given length) is defined as the potential difference across its ends divided by the current flowing through it. This is also known as Ohm’s Law. V R I Resistors • Conductors, semiconductors and insulators differ in their resistance to current flow. An ohmic*material of significant resistance placed in an electric circuit to control current or potential difference is called a resistor. • The units of resistance are volts per ampere (VA-1). However, a separate SI unit called the ohm Ω is defined as the resistance through which a current of 1 A flows when a potential difference of 1 V is applied. Since the term resistance refers to a small resistance, it is common for a resistor to have kilo ohm (kΩ) and mega ohm (MΩ) values. * An ohmic material is one that obeys Ohm’s law. Factors Affecting Resistance • The resistance of a conducting wire depends on four main factors: • length • cross-sectional area • resistivity • temperature Resistance of a Wire • It can be shown that when the temperature is kept constant L R A where R is the resistance in Ω, ρ is the resistivity specific to the material in Ω m, L is the length of the conductor in m, and A is the cross-sectional area of the conductor in m2. Resistance and Temperature • The resistance of a material increases with temperature because of the thermal agitation of the atoms it contains, and this impedes the movement of electrons that make up the current. • The increase in resistance can be shown as Rf = R0(1 + αT) where R0 equals the resistance at some reference temperature say 0 °C, Rf is the resistance at some temperature, T °C, above the reference temperature, and α is the temperature coefficient for the material being used. Superconductors • One interesting phenomenon of the effect of temperature on resistance is superconductivity. • In 1911, H. Kammerlingh Onnes found that mercury loses all its resistance abruptly at a critical temperature of 4.1 K. • When a material attains zero resistance at some critical temperature, it is called a superconductor. Ohm’s Law Revisited • The German physicist, Georg Simon Ohm (1787-1854), studied the resistance of different materials systematically. In 1826, he published his findings for many materials including metals. He stated that: Provided the physical conditions such as temperature are kept constant, the resistance is constant over a wide range of applied potential differences, and therefore the potential difference is directly proportional to the current flowing. • There are two relevant statements to be made here. Firstly, Ohm’s Law is not really a law but rather an empirical statement of how materials behave. Many materials are non-ohmic and this law is only applicable to ohmic conductors. Secondly, the law should not be written as R = V / I as this statement defines resistance. Ohm’s Law Revisited • The formula is commonly written as: V = IR where V is the potential difference across the resistor in volts V, I is the current in the resistor in amperes A and R is the resistance in ohms Ω. When written in this form R is understood to be independent of V. • As the current moves through the resistance of a device, it loses electric potential energy. The potential energy of a positive charge is less upon leaving the resistor than it was upon entering. We say that there is a potential drop across the device. Ohmic Materials • A graph of current versus the potential difference is a straight line. Devices that obey the linear relationship of the graph are said to be ‘ohmic devices’ or ‘ohmic conductors’. • There are very few devices that are ohmic although some metals can be if there is no temperature increase due to the heating effect of the current. However, many useful devices obey the law at least over a reasonable range. Remember that a resistor is any device with a potential difference and is not only restricted to the typical resistor used in the laboratory. It could be any useful electrical device – a filament lamp, a diode, a thermistor. • When a device does not obey Ohm’s Law, it is said to be non-ohmic. The filament lamp is non-ohmic because Ohm’s Law requires that the temperature remains constant, and this is not the case for an operating filament lamp. Current vs Voltage relationships for a few common devices Power Dissipation in Resistors • Electric power is the rate at which energy is supplied to or used by a device. It is measured in J/s or watts W. • When a steady current is flowing through a load such as a resistor, it dissipates energy in it. This energy is equal to the potential energy lost by the charge as it moves through the potential difference that exists between the terminals of the load. E p qV P or P IV t t Power and Ohm’s Law • Note that because V = IR and I = V/R we have the following relationships for power. • If a vacuum cleaner has a power rating of 500 W, it means it is converting electrical energy to mechanical, sound and heat energy at the rate of 500 J s-1. A 60 W light globe converts electrical energy to light and heat energy at the rate of 60 J s-1. Problems: • Tsokos, Pages 316 and 317, Questions 1 to 20 • Giancoli, Page 516, Odd Numbered Questions from #13 to 25 (Answers on page A-35 at the back of the book).

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# Topic 5.1 Electric Current and Resistance

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