1. P.1 Book 4 Section 2.4 Resistors in series and in parallel Christmas light Resistors in series Resistors in parallel Short circuit Check-point 8 Summary — Bulbs in series and in parallel 2.4Resistors in series and in parallel

2. P.2 Book 4 Section 2.4 Resistors in series and in parallel Christmas light What will happen if a bulb fails in this chain of Christmas lights? The other bulbs will continue to glow brightly.

3. P.3 Book 4 Section 2.4 Resistors in series and in parallel 1 Resistors in series Equivalent resistance of resistors in series Expt 2d

4. P.4 Book 4 Section 2.4 Resistors in series and in parallel Experiment 2d Equivalent resistance of resistors in series 2.5 Expt 2d - Equivalent resistance of resistors in series 1.Connect resistors R 1 and R 2 in series. 2.Measure current I of the circuit and voltage V across R 1 and R 2. Calculate equivalent resistance R eq by. 3.Repeat with other combinations of V, R 1 and R 2. VIVI Video

5. P.5 Book 4 Section 2.4 Resistors in series and in parallel 1 Resistors in series In a series circuit, R eq : equivalent resistance = sum of individual resistances in series 2.6 Series circuit Simulation R eq = R 1 + R 2 

6. P.6 Book 4 Section 2.4 Resistors in series and in parallel 1 Resistors in series Rewriting (1) in terms of current I flowing through each resistor: IR eq = IR 1 + IR 2 = I (R 1 + R 2 ) R eq = R 1 + R 2 Sum of voltage across each resistor = total voltage across the two resistors: V = V 1 + V 2 ……….. (1) Deriving R eq = R 1 + R 2 

7. P.7 Book 4 Section 2.4 Resistors in series and in parallel 1 Resistors in series In general, for any number of resistors connected in series, R eq = R 1 + R 2 + R 3 + … + R n Note: R eq of resistors in series > individual resistance  like joining two resistance wire to make a longer length

8. P.8 Book 4 Section 2.4 Resistors in series and in parallel 2 Resistors in parallel Equivalent resistance of resistors in parallel Expt 2e

9. P.9 Book 4 Section 2.4 Resistors in series and in parallel Experiment 2e Equivalent resistance of resistors in parallel 2.6 Expt 2e - Equivalent resistance of resistors in parallel 1.Connect resistors R 1 and R 2 in parallel. 2.Measure current I of the circuit and voltage V across R 1 and R 2. Calculate equivalent resistance R eq by. 3.Repeat with other combinations of V, R 1 and R 2. VIVI Video

10. P.10 Book 4 Section 2.4 Resistors in series and in parallel 2 Resistors in parallel In a parallel circuit, 1 R eq 1R11R1 1R21R2 = +  2.7 Parallel circuit Simulation

11. P.11 Book 4 Section 2.4 Resistors in series and in parallel 2 Resistors in parallel Rewriting (2) in terms of voltage across each resistor: 1 R eq 1R11R1 1R21R2 = + Sum of currents across each resistor = total current across the two resistors: I = I 1 + I 2............(2) Deriving 1/R eq = 1/R 1 + 1/R 2 V R eq VR1VR1 VR2VR2 = + 1R11R1 1R21R2 =V +

12. P.12 Book 4 Section 2.4 Resistors in series and in parallel 2 Resistors in parallel In general, for any number of resistors connected in parallel, Note: R eq of resistors in parallel < each individual resistance  like putting resistance wires side by side to make a wider piece of wire 1 R eq 1R11R1 1R21R2 = + + +... + 1R31R3 1Rn1Rn Series combination Example 9

13. P.13 Book 4 Section 2.4 Resistors in series and in parallel Example 9 Series combination Two resistors are connected in series to a battery. (a) Equivalent resistance = ? R eq = R 1 + R 2 = 3 + 6 = 9  (b) Voltage across the 6-  resistor = ? Current through each resistor = VRVR 9999 = = 1 A Voltage across the 6-  resistor = IR = 1  6 = 6 V

14. P.14 Book 4 Section 2.4 Resistors in series and in parallel 2 Resistors in parallel Parallel combination Example 10

15. P.15 Book 4 Section 2.4 Resistors in series and in parallel Example 10 Parallel combination Two resistors are connected in parallel to the battery: (a) Equivalent resistance of the two resistors = ?  R = 2  (b) Current through the 6-  resistor = ? Voltage across each resistor = 9 V Current through the 6-  resistor = VRVR 9696 = = 1.5 A 1R1R =+==+= 1313 1616 1212

16. P.16 Book 4 Section 2.4 Resistors in series and in parallel Example 10 (c) Total current in the main circuit = ? Parallel combination Current through 3-  resistor = VRVR 9393 = = 3 A Total current in the main circuit = sum of current through the two branches = 1.5 + 3 = 4.5 A

17. P.17 Book 4 Section 2.4 Resistors in series and in parallel 2 Resistors in parallel Complicated combination 2.8 Complicated circuit 2.9 Parallel and series combinations Simulation Example 11

18. P.18 Book 4 Section 2.4 Resistors in series and in parallel Example 11 Complicated combination Three resistors are connected in a network to a 12-V battery: (a) Total resistance of the network = ? R = equivalent resistance of B and C = + 1R1R 1616 1 12  R = 4  1414 = R is in series with A.  Total resistance = 4 + 8 = 12 

19. P.19 Book 4 Section 2.4 Resistors in series and in parallel Example 11 Complicated combination 12 = (b) Current through A = ? Current from battery = 1 A  Current through A = 1 A (c) Voltage across A = ? Voltage across A = 1  8 = 8 V

20. P.20 Book 4 Section 2.4 Resistors in series and in parallel Example 11 Complicated combination 4646 = = 0.67 A (d) Voltage across the parallel combination of B & C = ? Voltage = 12 – 8= 4 V (e) What is the current through (i) B, (ii) C ? Voltage across B = Voltage across C = 4 V (i) Current through B 4 12 = = 0.33 A (ii) Current through C

21. P.21 Book 4 Section 2.4 Resistors in series and in parallel 3 Short circuit The bulb lights up when the key is open. If the key is closed, Current flows through the key rather than the bulb. ( ∵ resistance of the wire ~ 0)  The bulb goes out and the connecting wires become very hot.  short-circuited

22. P.22 Book 4 Section 2.4 Resistors in series and in parallel 3 Short circuit Never connect the +ve and –ve terminal of a cell directly with a wire. ( ∵ The cell will go flat very quickly.) In a mains circuit, a short circuit can overheat the cables and cause a fire.

23. P.23 Book 4 Section 2.4 Resistors in series and in parallel Check-point 8 – Q1 Set-ups: to find how different connections of bulbs may result in different brightness. The power supply and four light bulbs are connected in series and in parallel respectively.

24. P.24 Book 4 Section 2.4 Resistors in series and in parallel Check-point 8 – Q1 Complete the table for the results. Circuit Equivalent resistance (higher or lower?) Current through the circuit (larger or smaller?) Brightness of bulbs (brighter or dimmer?) Higher Smaller Lower Larger DimmerBrighter

25. P.25 Book 4 Section 2.4 Resistors in series and in parallel Check-point 8 – Q2 If the switch is closed, what would happen to the bulb? The bulb would go out.

26. P.26 Book 4 Section 2.4 Resistors in series and in parallel Check-point 8 – Q3 Fill in the values of resistance in the blanks. 6 (a)

27. P.27 Book 4 Section 2.4 Resistors in series and in parallel Check-point 8 – Q3 Fill in the values of resistance in the blanks. 12 (b) 12

28. P.28 Book 4 Section 2.4 Resistors in series and in parallel Check-point 8 – Q3 Fill in the values of resistance in the blanks. 6 (c) 6

29. P.29 Book 4 Section 2.4 Resistors in series and in parallel Check-point 8 – Q3 Fill in the values of resistance in the blanks. 12 (d) 12

30. P.30 Book 4 Section 2.4 Resistors in series and in parallel Check-point 8 – Q4 Which has the highest equivalent resistance? All has the same equivalent resistance. 6 6 6 12

31. P.31 Book 4 Section 2.4 Resistors in series and in parallel 4 Summary — Bulbs in series and in parallel (i) One bulb glows brightly: voltage across the bulb = voltage of battery

32. P.32 Book 4 Section 2.4 Resistors in series and in parallel 4 Summary — Bulbs in series and in parallel (ii) Two identical bulbs in series glow dimly: If one is removed:  circuit broken  other bulb goes out Sum of voltages across two bulbs = voltage of battery Equally bright ( ∵ same current)

33. P.33 Book 4 Section 2.4 Resistors in series and in parallel (iii) Two identical bulbs in parallel glow brightly: If one is removed:  still an unbroken circuit through other bulb  continues to glow brightly Voltage across each bulb = voltage of the battery Two bulbs together draw twice as much current as a single bulb. 4 Summary — Bulbs in series and in parallel

34. P.34 Book 4 Section 2.4 Resistors in series and in parallel The End