DHS 10 D.C. Circuits (Lecture Notes & Tutorial)

1 9749 Physics (2024) Topic 15: D.C. Circuits Guiding Questions • How are symbols and diagrams used to represent real circuits? • How are the principles of charge and energy conservation applied to analyse circuits? 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. 9749 H2 Physics Topic 15 D.C. Circuits Year 5 (2024) DUNMAN HIGH SCHOOL

2 9749 Physics (2024) Topic 15: D.C. Circuits Introduction D.C. stands for direct current. It means current flowing only in one direction in a closed circuit. The magnitude of the current, however, may vary from time to time. The following are some examples of graphs representing the variation of direct current with time. In (a) and (b), the magnitudes of the current change with time. The currents in (a) and (b) flow in the opposite direction. In (c), the current flows with constant magnitude. We say, the current is a steady D.C. This chapter focuses mainly on the type of current shown in (c) – steady D.C. A simple D.C. circuit will usually comprise: a) source (s), e.g. batteries, cells b) switches c) resistors (or other components such as capacitors) d) measuring instruments such as voltmeter, ammeter, etc. time current time current time current (a) (b) (c)

3 9749 Physics (2024) Topic 15: D.C. Circuits (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 Standard circuit symbols are used to simplify circuit diagrams. Each circuit symbol represents an electrical device. The table below shows some common circuit symbols. Symbol Meaning Symbol Meaning cell / battery power supply switch ammeter voltmeter galvanometer filament lamp resistor variable resistor light dependent resistor thermistor diode potential divider earth aerial/antenna capacitor inductor wires crossing with no connection wires crossing with connection loudspeaker Application of Charge and Energy Conservation Principles in Circuit Analysis Charges cannot be created nor destroyed. This is the law of Conservation of Charge. Hence, the total charge that enters a junction per unit time (i.e. current entering) must be equal to the total charge that leaves the same junction per unit time (i.e. current leaving). Current Law: The sum of currents entering any junction in an electric circuit is always equal to the sum of currents leaving that junction (otherwise charge would build up at the junction). In the circuit below, the three currents by related by I = I1 + I2. V A I I1 I2 I R1 R2 E

4 9749 Physics (2024) Topic 15: D.C. Circuits Example 1 The diagrams show connected wires which carry currents I1, I2, I3 and I4. The currents are related by the equation I1 + I2 = I3 + I4. To which diagram does this equation apply? [N98/P1/Q16] A B C D Answer: ________ Answer: C Example 2 Calculate the currents IA, IB, IC, ID, IE, and IF as shown in the diagram below. Solution: Answer: IA = _______________ IB = _______________ IC = _______________ ID = _______________ IE = _______________ IF = _______________ I4 I3 I2 I1 I4 I3 I2 I1 I4 I3 I2 I1 I4 I3 I2 I1 2.4 mA IE ID IC 1.3 mA IB IF IA 3.7 mA 8.4 mA IA = 8.4 – 3.7 = 4.7 mA IB = 8.4 mA IC = 1.3 mA ID = 8.4 – 1.3 = 7.1 mA IE = 7.1 – 2.4 = 4.7 mA IF = 8.4 mA

5 9749 Physics (2024) Topic 15: D.C. Circuits The principle of Conservation of Energy states that energy cannot be created nor destroyed. Therefore, the electrical energy produced by the source should be equal to the sum of electrical energy consumed by all the components. Consider a closed circuit of electromotive force (e.m.f.) E and resistance R1 and R2. From the conservation of energy, Energy supplied by the source = Energy dissipated by the resistors (I E) t = (I2 R1) t + (I2 R2) t E = I R1 + I R2 i.e. E = V1 + V2 Voltage Law: In any closed loop in an electric c ircuit, the total e .m.f. E supplied equals to the total potential difference in that loop. In the circuit above, E = V1 + V2 Example 3 Referring to the circuit drawn, determine the value of the current I and the potential difference across each resistor. E = V1 + V2 + V3 E = I R1 + I R2 + I R3 2 = I (100) + I (600) + I (300) I = 1000 2 = 0.002 A Apply V = I R Potential difference across the 100  resistor = 0.002 x 100 = 0.2 V Potential difference across the 600  resistor = 0.002 x 600 = 1.2 V Potential difference across the 300  resistor = 0.002 x 300 = 0.6 V Check: Total emf in loop = total potential difference in loop Example 4 Referring to the circuit drawn, determine the value of I and R, the combined resistance in the circuit. loop ABCFEH, 2 = I1 (160) loop ABEH, 2 = I2 (4000) loop ABDGEH, 2 = I3 (32000) Therefore, I1 = 160 2 = 0.0125 A I2 = 4000 2 = 5.0  10-4 A I3 = 32000 2 = 6.25  10-5 A R2 R1 E I V1 V2 32000  4000  160  I1 I 2 V I2 I3 I 300  600  100  2 V V1 V2 V3 A B C D F E G H

6 9749 Physics (2024) Topic 15: D.C. Circuits Since I = I1 + I2 + I3, I = 13.1  10-3 A R = I V = 31013.1 2  = 153  Example 5 A battery with an e.m.f. of 20 V and an internal resistance of 2.0  is connected to resistors R1 and R2 as shown in the diagram. A total current of 4.0 A is supplied by the battery and R2 has a resistance of 12 . Calculate the resistance of R1 and the power supplied to each circuit component. Consider outer loop, E = I2 R2 + I r E - I r = I2 R2 20 – 4 (2) = I2 (12) I2 = 1 A Therefore, I1 = 4 – 1 = 3 A Consider upper loop, E= I1 R1 + I r E – I r = I1 R1 12 = 3 R1 R1 = 4 Ω Power supplied to R1 = (I1)2 R1 = 36 W Power supplied to R2 = (I2)2 R2 = 12 (c) solve problems using the formula for the combined resistance of two or more resistors in series In the circuit, the resistors R1 and R2 are said to be in series because the same current flows through both R1 and R2. From conservation of energy, E = V1 + V2 I1 r = 2  R1 R2 = 12 Ω 20 V I = 4 A I2 R2 R1