DC Circuits JPJC Notes

1 JURONG PIONEER JUNIOR COLLEGE 9749 H2 PHYSICS D.C. 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.

2 Introduction • In the previous topic on Current of Electricity, physical quantities such as electromotive force (e.m.f.), potential difference (p.d), current (I), resistance (R) and internal resistance (r) in electric circuits were discussed. • This topic on Direct Current (D.C.) Circuits involves electric circuits with current that flows in one direction. 1 Circuit symbols and diagrams (a) Candidates should be able to 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) Candidates should be able to draw and interpret circuit diagrams containing sources, switches, resistors, ammeters, voltmeters, and/or any other type of component referred to in the syllabus. 1.1 Circuit symbols wires crossed, wires joined, not joined junction of conductors signal lamp filament lamp fuse heater fixed resistor variable resistor light-sensitive light-emitting potential divider resistor (LDR) thermistor diode (LED) switch voltmeter ammeter galvanometer (open) Fig. 1 Circuit Symbols A V

3 2 Series and parallel arrangements (c) Candidates should be able to s olve problems using the formula for the combined resistance of two or more resistors in series. When two or more resistors are connected using connecting wires, the combined effect of these resistors can be represented by drawing a single resistor with a resistance called the c ombined resistance ( equivalent or effective resistance). The connecting wires are assumed to have negligible resistance. 2.1 Resistors in series Fig. 2 shows two resistors of resistance R1 and R2 connected in series between points A and B. The current passing through both resistors is the same. The corresponding potential difference (p.d.) across each of the resistors are V1 and V2. The p.d. across points A and B is V. Fig. 2 Resistors in series Applying VR= I to each of the resistors, we get: 11VR= I and 22VR= I ( ) 12 12 12 For a series connection, V V V RR RR =+ =+ =+ II I Rearranging: ( )12 VRR+= I ---------- (1) To find the combined resistance of R1 and R2, re-draw Fig. 2 using a single combined resistance R between points A and B. With the same p.d. V and current I through points A and B, we can apply VR= I between points A and B to get: VR = I ---------- (2) Comparing equations ( 1) and ( 2), we can easily calculate the combined resistance between A and B using: R = R1 + R2 This equation can be extended to as many resistors as there are in series: R = R1 + R2 + R3 + … + RN (where N is number of resistors connected in series) Note: The effective resistance is always greater than the largest resistance in the series network. R1 R2 I I A B V2 V1 V

4 (d) Candidates should be able to solve problems using the formula for the combined resistance of two or more resistors in parallel. 2.2 Resistors in parallel Consider 2 resistors, R1 and R2, connected in parallel, as shown in Fig. 3, Fig. 3 Resistors in parallel The p.d. V across both r esistors is the same because they are across the same 2 points A and B. Hence, 1 1 R V=I ---------- (3) 2 2 R V=I ---------- (4) To find the combined resistance of R1 and R2, re-draw Fig. 3 using a single combined resistance R between the points A and B. If the total current I is flowing between the points A and B, then the effective resistance R is given by R V=I ---------- (5) In the parallel circuit, the total current is the sum of the individual currents 12=+I I I ---------- (6) Combining equations (3), (4), (5) into (6), 12 V V V=+R R R Cancelling V, we can easily calculate the combined resistance using: 12 1 1 1=+R R R ------------ (7) This equation can be extended to as many resistors as there are in parallel. 12 1 1 1 1 NR R R R= + + + ... ------------ (8) (where N is number of resistors connected in parallel) Note: The effective resistance is always less than the smallest resistance in the parallel network. I1 R1 I2 R2 A B I I V

5 Example 1 Calculate the effective resistance across A and B in the network below. Effective resistance = 5 5 5 5 4 3++ = 3.9  Special cases: (i) Only 2 resistors in parallel: Equation (7) can be re-written as 12 12 RRR RR= + (ii) N number of identical resistors (R) in parallel: Equation (8) can be re-written as effective 1 1 1 1 N R R R R R= + + + =... effective RR N= 5  5  5  5  5  5  5  5  5  5  5  5  A B

6 For circuits involving many resistors connected in a combination of series and parallel network, more steps are required to determine the effective resistance of the overall circuit. Example 2 The circuit diagram shows a network of five identical resistors, each of resistance R. Calculate the effective resistance between points X and Y in terms of R. Solution: Effective resistance = 8 5R = 0.625 R Y X R R R 2R X R R Y X R 5/3 R Y X Y 5/8 R 2/3 R X Y

7 Some circuits are not easy to understand, and must be redrawn to see the series or parallel relationship between the resistors. Example 3 is an illustration: Example 3 Three resistors are connected as shown in the diagram using connecting wires of negligible resistance. Calculate the resistance between points P and Q. Solution: Hints: 1) Consider the three paths which a current from P can flow to Q. 2) Current flows from higher potential to lower potential. The above circuit can be arranged as three resistors in parallel. = ++= 545.0 3 1 2 1 1 11 R R 2.3 Variable resistors 1) Rheostat A