EJC Physics H215 DC Circuits - 1. Notes (2024)

Page 1 of 16 9749(2024) H2 Physics H215 D.C. Circuits – Notes H2 Topic 15 – D.C. Circuits A simple printed circuit board (PCB). A PCB is a mechanical support for the layout and electrical connection between electronic components. A PCB can have many layers sandwiched together, which allow many different connections between components within a small physical area. Content • Circuit symbols and diagrams • Series and parallel arrangements • Potential divider • Balanced potentials Learning Outcomes Candidates should be able to: (a) recall and use appropriate circuit symbols as set out in the ASE publication Signs, Symbols and Systematics (The ASE Companion to 16–19 Science, 2000) (b) draw and interpret circuit diagrams containing sources, switches, resistors, ammeters, voltmeters, and/or any other type of component referred to in the syllabus (c) solve problems using the formula for the combined resistance of two or more resistors in series (d) solve problems using the formula for the combined resistance of two or more resistors in parallel (e) solve problems involving series and parallel circuits for one source of e.m.f. (f) show an understanding of the use of a potential divider circuit as a source of variable p.d. (g) explain the use of thermistors and light-dependent resistors in potential divider circuits to provide a potential difference which is dependent on temperature and illumination respectively (h) recall and solve problems by using the principle of the potentiometer as a means of comparing potential differences 15.0 Introduction A direct current (D.C.) circuit is one where the direction of flow of current is maintained in the same direction. Such circuits are the basis for most (if not) all digital devices – the “power brick” connected to our laptops and the “mobile phone chargers ” convert household alternating current (A.C.) electricity into D.C. for use by the devices. Here, we learn how to represent real circuits using symbols and diagrams, and to apply conservation of (i) electric charge and (ii) energy when analysing circuits. A typical AC/DC adaptor. This particular “handphone charger” converts household electricity into a 5V D.C. source and supplies a maximum of 1 A to the device.

Page 2 of 16 9749(2024) H2 Physics H215 D.C. Circuits – Notes 15.1 Circuit Symbols cell switch junction of conductors battery of cells or earth galvanometer (a sensitive ammeter) or ammeter voltmeter oscilloscope power supply a.c. power supply thermistor fixed resistor variable resistor light- dependent resistor (LDR) potentiometer diode light-emitting diode (LED) lamp heater transformer 15.2.1 Resistors in Series When 2 or more resistors are connected in series, the effective resistance effR is the sum of the resistances. The electric current only has 1 possible path to flow. By conservation of charge, the same current flows through each of the resistors. 15.2.2 Resistors in Parallel The potential difference (p.d.) across each resistor that is connected in parallel is the same. Resistors that are connected in parallel will result in wire junctions at which the current splits up and re - combines where the branches meet again. 15.3 Junction Law Total current flowing into a junction must be equal to the total current flowing out of it. It is a consequence of charge conservation. It is also known as Kirchhoff’s 1st Law. In the figure on the right, I 1 + I 2 = I 3 + I 4 G … …

Page 3 of 16 9749(2024) H2 Physics H215 D.C. Circuits – Notes Example 1 Solution 123 123 123 By conservation of charge, so 11 1 1since p.d. is same across parallel branches, VV V V RR R R RR R R =++ =++ +I=I I +I Example 2 eff A B BA AB 1 11 R RR RR RR + = + = 1 B A BA eff AB A B R R RRR RR R R −   =  += + Note: Only for a pair of resistors in parallel, effR is equal to product of resistances sum of resistances . Example 3 Find the effective resistance of the following sets of resistors connected in parallel. Solution Layout 5 Ω 2.86 Ω 1 Ω 0.769 Ω Notes Identical resistors paired in parallel: is halved if convenient, use multiple times neater to apply is lower than lowest individual resistor in parallel branch 10 Ω 10 Ω 10 Ω 4 Ω 10 Ω 5 Ω 1 Ω 4 Ω 2 Ω 4 Ω The total current in the combination of resistors is I and the p.d. across the combination is V. Show that the total resistance R of the combination shown is given by the equation I V I1 I2 I3 Resistors A and B are connected in parallel. Express the effective resistance in terms of . Solution

Page 4 of 16 9749(2024) H2 Physics H215 D.C. Circuits – Notes Example 4 The 3 identical resistors are in parallel so eff eff 1 1113 3 R,RR RRRR += == + Note: For N number of identical resistors R, eff RR N= Example 5 Solution Option D has the lowest eff 2 2R. = Ω, so largest current in circuit. 15.4 Circuit Analysis Circuits can look complex. There are several guidelines we can refer to when analysing circuits: a. Check if it is a “closed circuit” or a circuit-segment where (conventional) current can flow from high electric potential to low electric potential. b. Identify segments of the circuit where combinations of resistors can be simplified as effective resistances. c. When comparing power output across components, useful to determine which quantity is kept constant (e.g. potential difference across resistors in parallel or current value through resistors in series) d. Where it is useful to think about potential differences across different parts the circuit, o ne single earth point can be added to the circuit to arbitrarily assign a zero potential value. A B A B A B A B A B A B 1 Ω 2 Ω 8 Ω 4 Ω Q P R Which of the following switch settings will result in the largest current in the circuit? P Q R A open open open B open closed closed C closed open closed D closed closed closed B: A: 1 Ω 2 Ω 1 Ω 2 Ω 4 Ω C: 1 Ω 2 Ω 4 Ω 8 Ω D: 1 Ω 2 Ω 4 Ω 8 Ω What is the effective resistance between A and B? Solution A B

Page 5 of 16 9749(2024) H2 Physics H215 D.C. Circuits – Notes Example 6 The potential at P is +10 V. The potential at Q is +4 V. Which option inaccurately describes the reading on the voltmeter and ammeter? Solution Option D is inaccurate. The potential difference between P and Q, ( ) ( )PQ P Q 10 4 6 VV VV= − =+ −+ = Since P is at a higher potential, (conventional) current flows from P to Q if there is uninterrupted path Notes: To short a component is to provide a path of zero resistance across it, usually via a wire. A shorted resistor can be ignored and treated as a connected wire segment. A shorted battery is dangerous because all available e.m.f. is applied as p.d. across the internal resistance, which causes rapid Joule heating within the battery physically, risking a fire hazard. 800 Ω 800 Ω V 800 Ω P Q X Y Z A R X Y Z V / V A / mA A closed open open 0 15 B open open open 6 0 C open closed closed 6 7.5 D closed closed open 0 5 800 Ω P Q Option B is accurate: 800 Ω An ideal voltmeter provides infinite resistance, PQ is a broken path so zero current. No current so the potential drop across the parallel resistors is zero ( ). So potential at R is same as potential at Q. Voltmeter reads the potential difference between P and R, 6 V. R V P Q Option C is accurate: R has the same potential as Q since Z is closed. Hence voltmeter reads the potential difference between P and R, VPR: 10 – 4 = 6 V V 800 Ω R In both O