TJC 16 Circuits 2026

2026 Temasek Junior College 1 Unit 16: CIRCUITS Learning Outcomes Candidates should be able to: (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 any other type of component referred to in the syllabus. (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 dependance 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. (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. tutor copy

2026 Temasek Junior College 2 1 Electrical circuit symbols LO(a)(b) cell battery switch resistor variable resistor lamp / bulb d.c. power fuse thermistor LED ammeter voltmeter heater LDR diode junction (wires joined) 1.1 Practical Circuits Circuit diagrams are used to show how electrical components are connected together to perform useful tasks. The connecting wires (leads) are drawn as straight lines in the diagram. All circuits need at least one source of energy. A cell is a single component that transfers chemical energy to electrical energy. The longer line represents the positive terminal of a cell. When cells are connected together they are called a battery. cell bulb resistor V + − A V wire crossing (no connection) galvanometer earth

2026 Temasek Junior College 3 1.1.1 Measurement of potential difference 1.1.2 Measurement of current The p.d. is the difference in potential between two points. To measure the p.d. between A and B of a resistor, the voltmeter must be connected in parallel to the resistor, i.e. one end to A, the other to B. An ideal voltmeter has infinitely high resistance so that it does not take any current from the circuit.  To measure the current flowing through a resistor, the ammeter must be connected so that the same current will flow through the ammeter as flows through the resistor. An ideal ammeter has zero resistance so that it does not change the current in the circuit. 

2026 Temasek Junior College 4 2 Resistance and resistivity 2.1 Resistance LO (c) Microscopically, resistance is due to frequent collisions of the drifting electrons with the vibrating ions in the lattice. When accelerated by an electric field, these free electrons gain kinetic energy but transfer part of this energy to the ions during collisions and hence slow down. This limits the current flow. i.e. VR I= SI unit is ohm (). One ohm is defined as the resistance of a conductor when the potential difference across the conductor is one volt per ampere of current flowing through it. (i.e. 1  = 1 V A-1) From I VR =  V = IR Conductors which give a constant ratio of V to I are known as ohmic conductors. They are said to obey Ohm’s Law. Ohm's Law states that the current through a metallic conductor is directly proportional to the potential difference across it, provided the temperature and other physical conditions are kept constant. Most resistors are not ohmic. Even for a metallic conductor, when current is increased with an increase in p.d., the temperature increases, thus increasing the resistance. The resistance is constant only when the temperature or the other physical conditions are kept constant, e.g. by immersing the specimen in a constant temperature water bath. Note: • The diagram below shows the circuit used to determine the resistance of a conductor. • A low resistance ammeter is connected in series with the conductor to measure the current I through it. A high resistance voltmeter is connected across the conductor to measure the potential difference V across it. + Conductor - battery A V Electrical resistance of a conductor is defined as the ratio of th e potential difference across the conductor to the current flowing through the conductor.

2026 Temasek Junior College 5 2.2 Resistivity LO (d) The resistance R of a uniform conductor of a given material at a given temperature is directly proportional to its length L and inversely proportional to its cross-sectional area A according to the equation LR A = where the constant of proportionality  is the resistivity and is a characteristic of the material. SI unit for resistivity is ohm metre ( m). The resistivity of a material is numerically equal to the resistance between opposite faces of a cube of the material, of unit length and unit cross-sectional area. The table below shows the resistivity for a selection of different materials. Substance Resistivity at 25 °C / m Uses Conductors Metals copper gold aluminium tungsten 1.72 × 10−8 2.42 × 10−8 2.82 × 10−8 5.51 × 10−8 connecting wires microphone contacts power cables light-bulb filaments Alloys steel constantan nichrome 20 × 10−8 49 × 10−8 100 × 10−8 standard resistors heating elements Semiconductors carbon germanium silicon 3.5 × 10−5 0.60 2300 resistors transistors transistors, chips Insulators glass polythene ~ 1013 ~ 1014 power grid insulators wire insulation Example 1: The overhead wire used to supply power to a factory is made of copper of resistivity 1.72  10−8 m and has cross-sectional area of 5.00 × 10−5 m2. Calculate the resistance of one kilometre length of the wire. Solution: R = l A  = -8 -5 (1.72×10 )(1000) 5.00×10 = 0.344  L I R A

2026 Temasek Junior College 6 2.3 I – V characteristics of electrical components LO (e) The variation in resistance can be represented by a plot of current I against p.d. V, called the I – V characteristics. The ratio of V to I gives the value of resistance R at that value of I. The ratio of V to I on such a curve gives the value of the resistance at that value of p.d. (a) Ohmic resistor: The ohmic resistor is a pure metallic conductor at constant temperature. It obeys Ohm’s law and has a constant resistance. Hence the I – V relationship is a straight line through the origin. LO (f) (b) Filament lamp: When the current is small, the temperature of the filament lamp is low so the resistance of the filament remains constant. When the current is large,