Ohm’s law Essay

An electronics factory needs resistors of 5 ohms and 15 ohms for a new electrical device. My task is to investigate how the resistance of a piece of wire depends on length and to find the length of the wire needed to make the required resistors, using only 4 volts. Introduction/Planning A selection of different wires made from constantan and nichrome and the usual laboratory apparatus will be available for me. Wire A – Constantan wire of approximate diameter 0. 3mm Wire B – Constantan wire of approximate diameter 0. 4mm Wire C – Constantan wire of approximate diameter 0. 3mm A constantan is an alloy whose resistance stays fairly constant when it becomes hot. In fact the resistance changes by less than 0. 5% even when the temperature rises by a few hundred degrees. Nichrome, along with other metals, is an alloy whose temperature does change appreciably when it becomes hot. Before starting my coursework, I have to find the variables in the experiment, safety aspects etc. I found that a number of things affect the resistance of a wire. Below is a list of factors and reasons why they affect the resistance of a wire. From this list of factors I have to make sure that these factors remain constant or excluded from the experiment. We are only investigating length but the other variables may change our outcomes. In electricity, resistance is the ratio of the potential difference (p. d. or voltage) across a conductor to the electrical current, which flows through it as a result. The unit of measurement is the ohm (O), this being the resistance of a conductor requiring a potential difference of 1 volt across its ends to produce a current of 1 ampere. For a given metal conductor at constant temperature the value is the same whatever the current (Ohm’s law), but rises if the temperature rises. Any conductor possessing resistance gives off heat when a current flows through it. Joule’s law describes this effect. Resistance occurs when the electrons travelling along the wire collide with the atoms of the wire. These collisions slow down the flow of electrons causing resistance. Resistance is a measure of how hard it is to move the electrons through the wire. Ohm’s law: The current flowing through a metal is proportional to the potential difference across it, provided that the temperature remains constant. We are going to use metals, which obey ohm’s law, metals which give us a constant value for resistance (gradient). Resistance (? ) = P. d across the wire (V) / Current through the wire (A) Current flows in an electric circuit in accordance with several definite laws. The basic law of current flow is Ohm’s law, named for its discoverer, the German physicist Georg Ohm. Ohm’s law states that the amount of current flowing in a circuit made up of pure resistances is directly proportional to the electromotive force impressed on the circuit and inversely proportional to the total resistance of the circuit. The law is usually expressed by the formula I = V/R, where I is the current in amperes, V is the electromotive force in volts, and R is the resistance in ohms Ohm’s law applies to all electric circuits for both direct current (DC) and alternating current (AC), but additional principles must be invoked for the analysis of complex circuits and for AC circuits also involving inductances and capacitances. A series circuit as on page 5, is one in which the devices or elements of the circuit are arranged in such a way that the entire current (I) passes through each element without division or branching into parallel circuits. When two or more resistances are in series in a circuit, the total resistance may be calculated by adding the values of such resistances. If the resistances are in parallel, the total value of the resistance in the circuit is given by the formula: In a parallel circuit, electrical devices, such as incandescent lamps or the cells of a battery, are arranged to allow all positive (+) poles, electrodes, and terminals to be joined to one conductor, and all negative (-) ones to another conductor, so that each unit is, in effect, on a parallel branch. The value of two equal resistances in parallel is equal to half the value of the component resistances, and in every case the value of resistances in parallel is less than the value of the smallest of the individual resistances involved. In AC circuits, or circuits with varying currents, circuit components other than resistance must be considered. If a circuit has a number of interconnected branches, two other laws are applied in order to find the current flowing in the various branches. These laws, discovered by the German physicist Gustav Robert Kirchhoff, are known as Kirchhoff’s laws of networks. The first of Kirchhoff’s laws states that at any junction in a circuit through which a steady current is flowing, the sum of the currents flowing to the point is equal to the sum of the currents flowing away from that point. The second law states that, starting at any point in a network and following any closed path back to the starting point, the net sum of the electromotive forces encountered will be equal to the net sum of the products of the resistances encountered and the currents flowing through them. This second law is simply an extension of Ohm’s law. The application of Ohm’s law to circuits in which there is an alternating current is complicated by the fact that capacity and inductance are always present. Inductance makes the peak value of an alternating current lag behind the peak value of voltage; capacitance makes the peak value of voltage lag behind the peak value of the current. Capacitance and inductance inhibit the flow of alternating current and must be taken into account in calculating current flow. The current in AC circuits can be determined graphically by means of vectors or by means of the algebraic equation, in which L is inductance, C is capacitance, and f is the frequency of the current. The quantity in the denominator of the fraction is called the impedance of the circuit to alternating current and is sometimes represented by the letter Z; then Ohm’s law for AC circuits is expressed by the simple equation I = V/Z. We know that all instruments have an error on its measurement, so the way to work out the percentage error is: Percentage error = (error / measured value) i 100 Conduction in metals In metals, atoms contain protons, nucleus and lose electrons which orbit around the nucleus. Below, I have investigated conduction in metals and how they affect resistance. METAL LATTICE (Electrons move in a random direction. ) METAL LATTICE (Electrons with power pack in a particular direction. ) Variables Length: If the length of the wire is increased then the resistance will also increase as the electrons will have a longer distance to travel and so more collisions will occur. Due to this, the length increase should be proportional to the resistance increase. Thickness: If the wire’s thickness is increased the resistance will decrease. This is because of the increase in the space for the electrons to travel through. Due to this increased space between the atoms, there should be fewer collisions. The number of free electrons changes from one material to another. The size of the ions changes from one material to another, this affects the current and therefore affects the resistance. The arrangement and size of the atoms change from one material to another. So if there is a kink in the wire this will change the thickness of the wire. Temperature: If the wire is heated up the atoms in the wire will start to vibrate because of their increase in energy.