H214 Current of Electricity - 1.0 Lecture Notes (1718)

Topic 14: Current of Electricity Page 1 of 32 9749 H2 Physics Lecture Notes Topic 14 Current of Electricity Content  Electric current  Potential difference  Resistance and resistivity  Electromotive force Learning Outcomes Candidates should be able to: (a) show an understanding that electric current is the rate of flow of charge (b) derive and use the equation I = nAvq for a current-carrying conductor, where n is the number density of charge carriers and v is the drift velocity (c) recall and solve problems using the equation Q = It (d) recall and solve problems using the equation V = W /Q (e) recall and solve problems using the equations P = VI, P = I2R and P = V2 / R (f) recall and solve problems using the equation V = IR (g) sketch and explain the I–V characteristics of various electrical components such as an ohmic resistor, a semiconductor diode, a filament lamp and a negative temperature coefficient (NTC) thermistor (h) sketch the resistance-temperature characteristic of an NTC thermistor (i) recall and solve problems using the equation R =ρl/A (j) distinguish between electromotive force (e.m.f.) and poten tial difference (p.d.) using energy considerations (k) show an understanding of the effects of the internal resistance of a source of e.m.f. on the termina l potential difference and output power.

Topic 14: Current of Electricity Page 2 of 32 9749 H2 Physics Lecture Notes Introduction Imagine a world without electricity. There would be no microwaves, no television, no hospitals or li fe- support systems, and worse for some, no wi -fi. In the classic science fiction movie, The Day the Earth Stood Still, an alien spacecraft neutralizes all e lectricity on Earth. As a result, society collapses, and technology is reduced to that of the 16th century. Electricity has become so vital in our daily life that we no longer notice its existence until we experience a power outage. In the future this inf luence can only grow. An understanding of the basic properties of electric current is important for its safe and effective use. 14.1 Electric Current & Charge When an electrical conductor is conducting electricity, an electric current is said to flow through them. These electric currents are made up of a net flow of tiny charge carriers (or charged particles) such as electrons (–ve), protons (+ve) or ions (+ve or –ve) through the conductor. In this section, we will set the foundation right by defining electric current and electric charge formally for future discussions. 14.1.1 Electric Current Electric current is one of the 7 base quantities. It is being introduced to quantify the rat e of flow of charged particles. The following table gives a simple summary of what you need to know about electric current. Physical Quantity Electric Current Definition Electric current is the rate of flow of charge. Type Scalar Symbol ܫ SI Unit Ampere (A) Formula In general If current is constant, then ܫ= ொ ௧ Graph Convention Direction of electric current is taken to be the direction of flow of positively charged particles. It is usually denoted by an arrow. ܫ= ܳ݀ ݐ݀

Topic 14: Current of Electricity Page 3 of 32 9749 H2 Physics Lecture Notes Note to self  It is important to note that current even though being given a direction and magnitude, is NOT a vector because it does not obey vector addition laws.  Current is being chosen as one of the 7 base quantities in place of charge because it is easier to define the unit of electric current, which is linked to electric charge then to derive the coulomb from the current.  Since = ௗொ ௗ௧ , current can be found by determining the gradient of a charge-time graph (Q-t graph). 14.1.1.1 (Conventional) Current Flow and Electron Current Flow By convention, the direction of electric current is taken to be the direction of flow of positively charged particles (conventional current), which means flowing from a point of higher potential to a point of lower potential as shown in Figure 1. In metals, where the charge carriers are electrons ( -ve), the electron flow is opposite to the direction of the conventional current. This type of current flow is known as the electron current flow. Fig. 1 Circuit diagram showing the direction of conventional current flow (left) and Electron Current Flow (right). **Note that in physics, most of the problems are being discussed via adopting the direction of conventional current unless otherwise stated.

Topic 14: Current of Electricity Page 4 of 32 9749 H2 Physics Lecture Notes 14.1.2 Electric Charge Electric charge is the physical quantity of matter that causes it to experience an electric force when it is in the vicinity of other electrically charged matter. However in this section, the focus is simply on the relation between charge and current. Physical Quantity Electric Charge Definition Charge is the property of a particle that causes an interaction of the particle with other charged particles and material of electrical nature. Type Scalar Symbol Q SI Unit Coulomb (C) One coulomb is the amount of charge which flows pass a point when a steady current of one ampere flows for one second. Formula In general If current is constant, then ܳ= ݐܫ Graph Useful Formula If N charge carriers each carrying charge q passes through a section of a circuit in time t, the average current can be expressed as: ܫ= ݈ܽݐ݋ݐ ܿℎ݁݃ݎܽ ܳ ݁݉݅ݐ ݐ= ݍܰ ݐ Note to self  A proton carries a charge of +1.60  10-19 C or e, where e denotes the elementary positive charge while an electron carries a charge of -1.60  10-19 C or –e; a helium nucleus carries a charge of 3.20  10-19 C or 2e, and so on.  Any charge can only exist as an integer multiple of the elementary charge e. ܳ= නܫ ݐ݀

Topic 14: Current of Electricity Page 5 of 32 9749 H2 Physics Lecture Notes  The amount of charge entering and leaving each junction is the same (or conserved) i.e. charges do not accumulate or disappear. This implies that the current remains constant along one single conductor. Similar to energy, charges obey the law of conservation: charges cannot be destroyed or created.  Examples of charge carriers Charge carriers Conductor Charge Example Ions Molten ionic solids Positive or negative Melted sodium chloride solid Electrolyte Positive or negative Car battery Gas Positive or negative Fluorescent tube Free electrons metal Negative wires Worked Example 1 A portable battery charger has a capacity of 7.49 × 10 4 C (20800 mAh). When it is being recharged, it draws a steady current of 1.5 A from the power supply. (a) Determine the time required to fully recharge the portable battery charger. Solution Using ܳ= ݐܫ, ݐ= 7.49 × 10ସ 1.5 = 49933.33 s = 13.9 hr (b) Determine the number of electron required to carry 7.49 × 104 C of charge. Solution Each electron carries an elementary charge e = 1.60  10-19 C. Using ܳ= ݁ܰ, ܰ= ܳ ݁= 7.49 × 10ସ 1.60 × 10ିଵଽ = 4.68 × 10ଶଷ Therefore, 4.68 × 1023 electrons are needed to carry this amount of charge.

Topic 14: Current of Electricity Page 6 of 32 9749 H2 Physics Lecture Notes 14.1.3 Deriving I = nAvq for a current-carrying conductor When no potential difference is applied across a conductor, its mobile charge carriers undergo random motion similar to gas molecules in the air as shown in Fig. 2(a). Fig. 2 (a) Charge carriers in random motion (left) and (b) Charge carriers in random motion with axial drift when a potential difference is applied (right) Taking metal as an example, eac h atom contributes one or more free electrons to form the ionic bonds which hold the positive ions together in a metallic structure. The electrons are not attached to any particular ion but are mobile within the boundary of the lattice. As they are movin