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AP1200_Ch5_Electricity-2008

# AP1200_Ch5_Electricity-2008 - AP1200 Foundation Physics...

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AP1200 Foundation Physics Limited wisdom and incorrect predictions: "This 'telephone' has too many shortcomings to be seriously considered as a means of communication. The device is inherently of no value to us." -- Western Union internal memo, 1876. "But what . .. is it good for?" -- Engineer at the Advanced Computing Systems Division of IBM, 1968, commenting on the microchip. Chapter 5: Electricity In this Chapter we will discuss electric fields, Gauss’s law, electric potential, capacitance, currents and the resistance of materials. 5.1 Electric Current Current rate of flow of charge through a material A current flow depends on the properties of the material and the potential difference (voltage) across the material. Consider an area A (Fig. 5.1) through which positive charges are flowing perpendicularly. The rate of flow of charge through this area is the electric current, I . + + + + + A I Fig. 5.1 Current Thus, the current is the number of charges passing through area A in each time interval: dt dQ I = (5.1)

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The unit of current is the ampere : 1 A = 1 coulomb per second. The coulomb (C) is the unit of charge. The charge of an electron is 1.6 × 10 -19 C, for example. The charges passing through area A in Fig. 5.1 can be positive or negative. It is convention to define current as flowing in the direction of the positive charges . In most metal conductors, it is actually negatively charged electrons that move. Hence the direction of current is in the opposite direction to the movement of electrons. For example, if you connect a battery to a light bulb, we say that current flows from the positive terminal of the battery, through the bulb and back to the negative terminal of the battery. But in fact, the current arises as a flow of electrons and these travel in the opposite direction (Fig. 5.2). I - - - - - - - - - - - - - - - Fig. 5.2 Direction of Current It is common to refer to the moving charge as charge carriers . For metals, we have negative charge carriers, i.e. electrons, but some materials have positive charge carriers and some materials have both. If the ends of a conducting wire are attached to a battery, an electric field is created in the wire; this field exerts a force on the electrons, causing them to move. Suppose the charge carriers move with a drift speed of v d (Fig. 5.3). A v d q Δ x Fig. 5.3 Current in a Wire
Assume that the charge carriers move a distance Δ x in time Δ t . The charge passing through area A during this time interval Δ t will be: xq nA Q Δ = Δ where n is the number of charge carriers per unit volume and q is the charge on each carrier. But , so t v x d Δ = Δ t q nAv Q d Δ = Δ and hence q nAv t Q I d = Δ Δ = (5.2) Example – drift speed in a copper wire An electrical wire in a home typically has a conductor diameter of 2mm. If such a wire carries a current of 10A, what is the drift speed? The density of copper is 8950 kg/m 3 .

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AP1200_Ch5_Electricity-2008 - AP1200 Foundation Physics...

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