RI Chap 16 Circuits Lecture Notes

16 CIRCUITS H2 Physics 9478 Content Page 16.1 Circuit symbols and diagrams 2 16.2 Resistance, resistivity, and internal resistance 4 16.3 Resistors in series and in parallel 16 16.4 RC circuits with d.c. source 42 16.5 Appendix 49 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, lρ=R 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 constant 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 a constant 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. (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 ( )τ= −0 exp /xx t or ( )[ ]τ=−−0 1 exp /xx t , where τ = RC is the time constant.

Page | 2 16.1 Circuit symbols and diagrams  Circuit Symbols The following is a list of circuit symbols used in the syllabus. Category Component Circuit Symbol Function of Component Wires and Connections Wire To pass current from one part of a circuit to another. Wires that are connected This symbol is used in circuit diagrams where wires cross to show that they are connected (joined). Wires that are not connected In complex circuit diagrams it is often necessary to draw wires crossing even though they are not connected. You may prefer to use the 'hump' symbol shown on the right, because the simple crossing on the left looks like connection. Power Supplies Cell Supplies electrical energy. Single cells are often wrongly called batteries; strictly, a battery comprises two or more cells joined together. The side with the longer line is the positive terminal. Battery Supplies electrical energy. A battery is more than one cell joined together. The side with the longer line is the positive terminal. D.C. supply Supplies electrical energy. A.C. supply Supplies electrical energy. Earth (ground) A connection to earth. For many electronic circuits, this is the 0 V (zero volt) of the power supply, but for mains electricity and some radio circuits, it really means the earth. It is also known as ground. Lamps Lamp A transducer which converts electrical energy to light. This symbol is used for a lamp providing illumination, e.g. a car headlamp or torch bulb. Indicator or light source + −

RAFFLES INSTITUTION YEAR 56 PHYSICS DEPARTMENT 3 | Page Category Component Circuit Symbol Function of Component Switches On-Off switch An on-off switch allows current to flow only when it is in the closed (on) position. Resistors Fixed resistor A resistor restricts the flow of current, for example to limit the current passing through a device. Variable resistor This type of variable resistor (e.g. a rheostat) is usually used to vary current through a circuit. Light Dependent Resistor (LDR) An LDR is a semiconductor device. Its resistance decreases from several 10 6 Ω in the dark to several 102 Ω as the brightness (illumination) of light falling on it increases. Thermistor A thermistor is a semiconductor device. The resistance of most thermistors decreases from 10 kΩ to 2 kΩ as its temperature increases from − 55 °C to 70 °C. Such thermistors are called negative temperature coefficient or N.T.C. thermistors. Diodes Diode A device which only allows current to flow in one direction. Light Emitting Diode (LED) A transducer which converts electrical energy to light. Capacitors Capacitor A capacitor is used for storing electric charge. Meters Voltmeter A voltmeter is used to measure potential difference. Ammeter An ammeter is used to measure current. Galvanometer A galvanometer is a very sensitive meter which is used to detect tiny currents, and changes in direction of current. Ohmmeter An ohmmeter is used to measure resistance. Most digital multimeters (DMMs) have an ohmmeter setting. Fig. 16.1 V A Ω

Page | 4  Circuit Diagrams Circuit diagrams are drawn with wires and electrical components. Only essential features of a circuit are drawn, and all electrical devices are represented by standard symbols. The figure below shows an actual circuit arrangement with its circuit diagram. Note that inter-connected wires must be indicated with a dot (•). Fig. 1.1 Fig. 16.2 16.2 Resistance, resistivity, and internal resistance  Resistance R and its unit. In equation form, electrical resistance is given by Definition The resistance of a circuit component is defined as the ratio of the potential difference across it to the current in it. A V

RAFFLES INSTITUTION YEAR 56 PHYSICS DEPARTMENT 5 | Page = I VR The S.I. unit for resistance is the ohm, Ω. The ohm is the resistance of a circuit component when a potential difference of one volt across it causes a current of one ampere to flow through it ( −Ω= 11 1 V A ). Determining R A simple way to determine the resistance of a circuit component is to connect 1. an ammeter, assumed to have no resistance, in series with the component and 2. a voltmeter, assumed to have an infinite resistance, in parallel with the component as shown in Fig. 16.3. The ammeter measures the current flowing through the component and the voltmeter measures the p.d. across it. The resistance can thus be determined using = I VR . Fig. 16.3 Example 1 A car stereo system draws a current of 400 mA when connected to a 12.0 V battery. (a) Calculate the resistance of the stereo system. (b) The stereo is left playing from the battery for several hours while the engine is turned off. The radio can continue to operate until the current drops to 320 mA. Calculate the p.d. across the stereo when it stops playing. Solution R E - + I V A

Page | 6 Example 2 The graph below shows the relationship between the direct current I in a certain conductor and the potential difference V across it. When V < 1.8 V, the current is negligible. Determine the resistance of the conductor when the p.d. is 3.0 V. Solution  Re