ACJC Currents Lecture Notes

Anglo-Chinese Junior College Lecture Notes Currents H2 (9478) JC1 2025 Page 1 of 22 Currents Guiding Questions Learning Objectives 1. How does the macroscopic phenomenon of current flow relate to the movement of microscopic charges? (a) show an understanding that electric current is the rate of flow of charge and solve problems using = QI t . (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. 2. What happens to energy in an electrical circuit? (c) recall and solve problems using the equation for potential difference in terms of electrical work done per unit charge, = WV Q . (d) recall and solve problems using the equations 𝑃=𝑉𝐼, 𝑃=𝐼2𝑅 and 2 = VP R . (e) distinguish between electromotive force (e.m.f.) and potential difference (p.d.) using energy considerations. 3. How can we describe alternating current, e.g. mathematically and graphically? (f) show an understanding and use the terms period, frequency, peak value and root-mean-square (r.m.s.) value as applied to an alternating current or voltage. (g) represent an alternating current or an alternating voltage by an equation of the form 0 sin=x x t . (h) deduce that the mean power in a resistive load is half the maximum (peak) power for a sinusoidal alternating current. (i) distinguish between r.m.s. and peak values , and recall and use 0 .. 2 =r m s II and 0 .. 2 =r m s VV for the sinusoidal case. (j) explain the use of a single diode for the half -wave rectification of an alternating current.

Anglo-Chinese Junior College Lecture Notes Currents H2 (9478) JC1 2025 Page 2 of 22 Nature of Science Moment – Who invented Electricity? Thales of Miletus – Greek philosopher Thales of Miletus discovered that rubbing amber (fossilized tree sap) with animal fur would attract objects like feathers. Without truly knowing it, he had noticed the effects of magnetism and static electricity. William Gilbert – In his book “De Magnete”, English scientist William Gilbert coined the term ‘electricus’ in 1600, which means ‘amber -like’. Polymath Sir Thomas Browne later altered the word slightly, changing it to ‘electricity’ in 1646. Stephen Gray – Stephen Gray discovered the difference between electrical insulators and conductors, finding that electricity would “flow along wires”. Ewald Georg von Kleist and Pieter van Musschenbroek – In 1745, the two scientists invented the Leyden Jar. This was a key invention in the build- up of our understanding of electricity. The Leyden Jar was a glass jar or vial coated on the inside and outside with metal foil. The Leyden Jar was an early capacitor, or device for storing an electric charge. This device was able to store electricity. Scientists William Watson, Henry Cavendish and Charles A Coulomb all use the Leyden Jar in the key experiments with electricity, in the few years before Benjamin Franklin’s kite experiment. Benjamin Franklin – In 1752, Franklin proved that lightning consisted of electricity by flying a kite during a thunderstorm. A metal key was tied to the string of the kite to conduct the electricity from lightning, and it worked (giving him a shock). This experiment is credited with sparking the idea of using electricity as a power source. Luigi Galvani – Galvani discovered ‘animal electricity’ when in 1786 he discovered by accident that the spinal cords of a frog carried an electric charge. He compared the frog’s muscles to a Leyden Jar. Alessandro Volta – Alessandro Volta was an Italian physicist who invented the first electric battery known as the ‘voltaic pile’ in 1800. This device produced a steady flow of electrical current and was a significant advancement in the field. Volta repeated and checked Galvani’s experiments and started to doubt that the conductions were caused by specific electricity intrinsic to the animal legs or other body parts. He believed that the contractions depended on the metal cable Galvani used to connect the nerves and muscles in his experiments. Michael Faraday – Faraday, an English scientist, made groundbreaking discoveries in the field of electromagnetism. He formulated the laws of electromagnetic induction and demonstrated the generation of electricity through moving magnetic fields. Faraday’s work laid the foundation for the development of electric generators and transformers.

Anglo-Chinese Junior College Lecture Notes Currents H2 (9478) JC1 2025 Page 3 of 22 Nature of Science Moment – Who invented Electricity? The Galvani-Volta Debate Thomas Edison – Edison, an American inventor, is renowned for his contributions to the practical application of electricity. He developed the first successful practical electric light bulb and established the world’s first electric power distribution system, which was crucial in bringing electricity into homes and businesses. Nikola Tesla – Tesla, a Serbian-American inventor and engineer, made numerous advancements in the field of electrical engineering. He pioneered alternating current (AC) power transmission, which revolutionized the way electricity is generated, transmitted and distributed. References: BBC Science Focus – Who invented electricity https://www.sciencefocus.com/science/who-invented-electricty https://backyardbrains.com/experiments/Galvani_Volta

Anglo-Chinese Junior College Lecture Notes Currents H2 (9478) JC1 2025 Page 4 of 22 1 Relationship between current and charge 1.1 Electric current The SI unit for electric current is ampere (A). Examples of electric current: 1. Flow of electrons in a conductor such as a copper wire. 2. A beam of electrons in a television picture tube. 3. For gases and electrolytes (with both positive and negative charges), electric current is the sum of the flow of positive charges in one direction and the flow of negative charges in the opposite direction. Both positive and negative charges produce current in same direction (direction of flow of positive charges). How does the macroscopic phenomenon of current flow relate to the movement of microscopic charges? The current is the charge per unit time (rate of charge) flowing through a cross- sectional area. Average current Iave is the amount of charge Q that flows through a cross - sectional area A in a time interval t. =ave QI t Instantaneous current I is the rate of charge flow through a cross-sectional area A (if rate of charge flows varies with time). = dQI dt +−=+I I I I+ I + − A I Fig. 1.1

Anglo-Chinese Junior College Lecture Notes Currents H2 (9478) JC1 2025 Page 5 of 22 1.2 Electric charge and the coulomb Electric charge is the physical property that causes it to experience a force when placed in an electromagnetic field. The charges of free-standing particles are integer multiples of the elementary charge e; we say that electric charge is quantised. There are two types of electric charges: • positive (commonly carried by protons) • negative (commonly carried by electrons). An object with an absence of net charge is neutral. Coulomb is the SI unit of charge. It is the charge transferred by a steady current of one ampere in one second. (1 C = 1 A s). If constant current I is flowing for a time