ACJC Circuits Lecture Notes

Anglo-Chinese Junior College Lecture Notes Circuits H2 (9478) JC2 2026 Page 1 of 41 Circuits Guiding Questions Learning Objectives 1. How are symbols and diagrams used to represent real circuits? (a) recall and use appropriate circuit symbols. (b) draw and interpret circuit diagrams containing sources, switches, resistors (fixed and variable), ammeters, voltmeters, lamps, thermistors, light -dependent resistors, diodes, capacitors and/or any other type of component referred to in the syllabus 2. How are current, voltage, and resistance related in an electrical circuit? (c) define the resistance of a circuit component as the ratio of the potential difference across the component to the current in it, and solve problems using the equation 𝑉 = 𝐼𝑅. (d) recall and solve problems using the equation relating resistance to resistivity, length and cross -sectional area, = lR A . (e) sketch and interpret the 𝐼-𝑉 characteristics of various electrical components in a d.c. circuit, such as an ohmic resistor, a semiconductor diode, a filament lamp and a negative temperature coefficient (NTC) thermistor. (f) explain the temperature dependence of the resistivity of typical metals (e.g. in a filament lamp) and semiconductors (e.g. in an NTC thermistor) in terms of the drift velocity and number density of charge carriers respectively. (g) show an understanding of the effects of the internal resistance of a source of e.m.f. on the terminal potential difference and output power. 3. How are the principles of charge and energy conservation applied to analyse circuits? (h) solve problems using the formula for the combined resistance of two or more resistors in series. (i) solve problems using the formula for the combined resistance of two or more resistors in parallel. (j) solve problems involving series and parallel arrangements of resistors for one source of e.m.f., including potential divider circuits which may involve NTC thermistors and light-dependent resistors. (k) solve problems using the formulae for the combined capacitance of two or more capacitors in series and in parallel.

Anglo-Chinese Junior College Lecture Notes Circuits H2 (9478) JC2 2026 Page 2 of 41 (l) describe and represent the variation with time, of quantities like current, charge and potential difference, for a capacitor that is charging or discharging through a resistor, using equations of the form 𝑥 = 𝑥0 exp(−𝑡/𝜏) or 𝑥 = 𝑥0[1 − exp(−𝑡/𝜏)], where 𝜏 = 𝑅𝐶 is the time constant.

Anglo-Chinese Junior College Lecture Notes Circuits H2 (9478) JC2 2026 Page 3 of 41 1. Circuit Symbols and Diagrams A standard set of common symbols is used to draw a circuit diagram. Groupings of symbols should improve clarity and aid in the understanding of the electric circuit. cell switch battery of cells or earth power supply alternating current (a.c.) power supply junction of wires lamp How are symbols and diagrams used to represent real circuits?

Anglo-Chinese Junior College Lecture Notes Circuits H2 (9478) JC2 2026 Page 4 of 41 fixed resistor variable resistor thermistor light-dependent resistor (LDR) potentiometer diode voltmeter light-emitting diode (LED) ammeter galvanometer capacitor

Anglo-Chinese Junior College Lecture Notes Circuits H2 (9478) JC2 2026 Page 5 of 41 2. Resistance 2.1 Electrical Resistance The SI unit of resistance is ohm (). The ohm is defined as the electrical resistance between two points of a conductor through which a steady current of 1 A flows when a constant potential difference of 1 V is maintained across it. Hence, 1  = 1 V A−1. 2.1.1 Ohm’s Law By Ohm’s law, where graph is a straight line that passes throu gh the origin V k V V    =− By definition of resistance, 1 where is a constant VR kk = = How are current, voltage, and resistance related in an electrical circuit? The resistance R of a conductor is defined as the ratio of potential difference V across the conductor and current I in it. Ohm’s law states that the current I flowing through a conductor is directly proportional to the potential difference V applied across the conductor provided that the physical conditions (such as temperature, stress etc) remain constant. VR  =

Anglo-Chinese Junior College Lecture Notes Circuits H2 (9478) JC2 2026 Page 6 of 41 2.1.2 Resistivity Resistance of a conductor R is directly proportional to its length, l and inversely proportional to its cross-sectional area A. At room temperature, • Metal:  = 10−13  m • Semiconductor:  = 10−4 to 105  m • Insulator:  = 1013 − 1016  m Example 2.1 Two wires A and B of circular cross section are made of the same metal and have equal lengths, but the resistance of wire A is three times greater than that of wire B. (a) Determine the ratio of their cross-sectional areas. (b) Determine the ratio of their radii. Solution: (a) l ,l 2 are constants 3 3 A B BA B A R where A R A where A rRA A R AR   = == == (b) 2 2Sin , 3 1.73 BB AA B A Arce Ar r r = == Resistivity is an electrical property of a material, and its value gives the electrical resistance of a conductor of unit cross -sectional area and unit length, made from that material. where  is the resistivity of the material l l R A RA   = = The SI unit of resistivity is ohm metre ( m)

Anglo-Chinese Junior College Lecture Notes Circuits H2 (9478) JC2 2026 Page 7 of 41 Example 2.2 A car headlight filament is made of tungsten and has a resistance of 0.35 . The resistivity of tungsten is 5.6 x 10−8  m. If the filament is a cylinder 4.0 cm long (it may be coiled to save space), what is its diameter? Solution: l l R A A R   = = Assuming that the wire is perfectly cylindrical so A can be expressed as 2 4 D . 2 82 5 4 4 4 5 6 10 40 10 035 90 10 m D R D R    −− − = == = l l ( . )( . ) ( . ) . 2.2 I−V Characteristics Resistance R is affected by 2 opposing mechanisms: 1. increase in rate of collision of free electrons (charge carriers) with lattice ions – R increases 2. increase in number of free electrons due to bound electrons being freed – R decreases 2.2.1 A metallic conductor at constant temperature (linear conductor) Fig. 2.1 • All metals contain lattice ions (which vibrate continuously about their equilibrium positions) and free electrons (number density is characteristic of each metal). • The I−V characteristic graph is a straight line passing through the origin. Thus, I  V ie resistance R is constant. Metallic conductors obey Ohm’s law at constant temperature. I V low resistance high resistance 0 0

Anglo-Chinese Junior College Lecture Notes Circuits H2 (9478) JC2 2026 Page 8 of 41 • When p. d. V increases, ➢ acceleration of electrons increase, drift velocity increases, rate of flow of electrons increases, thus electric current I increases. ➢ as free electrons move, they collide with the vibrating lattice ions, o which gains kinetic energy and vibrate with larger amplitudes (natural frequency remains constant), the larger the amplitude, the greater is the chance of collision and obstructing the path of the free electrons (so by right R should increase), o The number of bound electrons freed during collision with free electrons does not increase significantly (as metals has a large number of free electrons), o In this type of metals, kinetic energy gained by lattice ions is dissipated quickly to the surroundings, hence temperature and amplitude of lattice ions remain constant, hence R is constant. 2.2.2 A filament lamp (non-linear conductor) Fig. 2.2 • A filament is a thin metal wire housed inside a glass enclosure filled with inert gas. ➢ At low p.d. (